NCERT Solutions Class 7 Mathematics Ganita Prakash 1 Chapter 02 Arithmetic Expressions

Question 1. Mallika spends ₹25 every day for lunch at school. Write the expression for the total amount she spends on lunch in a week from Monday to Friday.
Answer: Mallika buys her lunch on 5 days from Monday to Friday. Since each day costs ₹25, the full expression for the amount she spends is 5 x 25.
In simple words: If something costs 25 rupees each day and you buy it for 5 days, multiply 5 by 25.

Exam Tip: Form expressions by identifying what changes (number of days) and what stays the same (cost per day), then multiply them together.

Question 2. Choose your favourite number and write as many expressions as you can having that value.
Answer: Let us pick the number 20. Here are many expressions with this value:
15 + 5
30 - 10
4 x 5
100 / 5
2 x (7 + 3)
(6 x 5) - 10
18 + (10 / 5)
In simple words: You can make the same number in lots of different ways by using addition, subtraction, multiplication, and division together.

Exam Tip: Show at least 5-6 different expressions for full marks. Use different operations - don't just add or subtract.

Question 3. Fill in the blanks to make the expressions equal on both sides of the = sign. (a) 13 + 4 = __ + 6
Answer: Start by calculating the left side: 13 + 4 = 17. The right side needs to equal 17 as well. So we need __ + 6 = 17. Subtracting 6 from both sides gives us the blank value of 11.
In simple words: Work out what the left side equals first. Then find what number you need on the right side to make both sides the same.

Exam Tip: Always calculate one side completely first. Then use subtraction or addition to find the missing number.

Question 4. (b) 22 + __ = 6 x 5
Answer: Work out the right side first: 6 x 5 = 30. Now the left side must also equal 30. We need 22 + __ = 30. Subtract 22 from 30 to find the blank, which is 8.
In simple words: Find the value of the right side. Then see what number you must add to 22 to get that value.

Exam Tip: When you have multiplication or division on one side, work that out before finding the missing number.

Question 5. (c) 8 x __ = 64 / 2
Answer: Calculate the right side: 64 / 2 = 32. Now we need 8 x __ = 32. Divide 32 by 8 to get the blank, which equals 4.
In simple words: Work out the division first. Then find what number times 8 gives you that answer.

Exam Tip: If the blank is being multiplied, divide to find it. If it's being divided, multiply to find it.

Question 6. (d) 34 - __ = 25
Answer: We need to find the number being subtracted from 34 to get 25. Subtract 25 from 34 to find the blank: 34 - 25 = 9.
In simple words: If you subtract something from 34 and get 25, that something must be 9.

Exam Tip: When a number is being subtracted, always subtract the result from the starting number.

Question 7. Arrange the following expressions in ascending (increasing) order of their values. (a) 67 - 19 (b) 67 - 20 (c) 35 + 25 (d) 5 x 11 (e) 120 / 3
Answer: First find each value:
(a) 67 - 19 = 48
(b) 67 - 20 = 47
(c) 35 + 25 = 60
(d) 5 x 11 = 55
(e) 120 / 3 = 40

Now arrange from smallest to largest: 40, 47, 48, 55, 60.

So the expressions in order are: 120 / 3, 67 - 20, 67 - 19, 5 x 11, 35 + 25.
In simple words: Work out all the answers first. Then arrange them from the smallest number to the biggest number.

Exam Tip: Write down each value clearly before sorting. Use a chart if there are many expressions to compare.

Question 8. Which is greater? 1023 + 125 or 1022 + 128?
Answer: Compare the two expressions part by part. The first has 1023 while the second has 1022 - so the first starts with 1 more. The first adds 125 while the second adds 128 - so the second adds 3 more. The first started 1 ahead but the second adds 3 more, so the second is bigger by 2. Therefore 1022 + 128 is greater than 1023 + 125. You can verify: 1023 + 125 = 1148 and 1022 + 128 = 1150. Since 1150 is bigger, 1022 + 128 is greater.
In simple words: When comparing two sums, look at how much bigger the first numbers are and how much bigger the second numbers are, then add those differences.

Exam Tip: You don't always need to calculate both sums completely. Smart comparison using difference analysis saves time.

Question 9. Which is greater? 113 - 25 or 112 - 24?
Answer: Compare the two expressions. The first one starts with 113, and the second starts with 112 - so the first starts with 1 more. The first subtracts 25, and the second subtracts 24 - so the first subtracts 1 more. Even though the first starts with 1 more, it also takes away 1 more. These two changes cancel out, so both expressions end up with the same value. You can verify: 113 - 25 = 88 and 112 - 24 = 88. They are equal.
In simple words: Both expressions equal 88. Getting 1 more at the start but taking away 1 more at the end cancels out.

Exam Tip: Look for how changes in different parts balance each other out rather than calculating everything.

Question 10. Use '>', '<' or '=' in each of the following expressions to compare them. Can you do it without complicated calculations? Explain your thinking in each case. (a) 245 + 289 ___ 246 + 285
Answer: The left side has 245, while the right side has 246 - the right side starts with 1 more. The left side adds 289, while the right side adds 285 - the left side adds 4 more. The left side gains 4 more than the right side in its second part, while the right side only gains 1 more in the first part. So the left side ends up with 3 more overall. Therefore 245 + 289 > 246 + 285.
In simple words: Compare each part. The left side adds 4 more than the right side does, even though it starts 1 less.

Exam Tip: Break down the comparison into first numbers and second numbers. Find the net difference without fully calculating.

Question 11. (b) 273 - 145 ___ 272 - 144
Answer: Look at each number. The left side starts with 273 and the right side starts with 272 - the left is 1 more. The left side subtracts 145 and the right side subtracts 144 - the left subtracts 1 more. These differences cancel out perfectly: gaining 1 in the first number but losing 1 more in the subtraction means both sides end up equal. Therefore 273 - 145 = 272 - 144.
In simple words: The left side starts 1 higher but takes away 1 more. These balance out, making both sides equal.

Exam Tip: When comparing subtraction, pay attention to both how much you start with and how much you subtract.

Question 12. (c) 364 + 587 ___ 363 + 589
Answer: The left side has 364 while the right side has 363 - the right side is 1 less. The left side adds 587 while the right side adds 589 - the right side adds 2 more. The left side loses 1 in the first part while the right side gains 2 in the second part. So overall the right side is 1 more. Therefore 364 + 587 < 363 + 589.
In simple words: Even though the left side starts with a bigger first number, the right side adds 2 more in the second number, which makes up for it and gives the right side a bigger total.

Exam Tip: Look at the net change. If one side loses in one part but gains more in another part, those balance to decide which is bigger.

Question 13. (d) 124 + 245 ___ 129 + 245
Answer: Notice that both sides add the same number, 245. So we just need to compare the first numbers: 124 versus 129. Since 124 is smaller than 129, the left side is smaller overall. Therefore 124 + 245 < 129 + 245.
In simple words: When both sides add the same thing, just compare the other numbers.

Exam Tip: If one part is identical on both sides, ignore it and focus on what is different.

Question 14. (e) 213 - 77 ___ 214 - 76
Answer: The left side starts with 213 and the right side starts with 214 - the right side is 1 more. The left side subtracts 77 and the right side subtracts 76 - the left side subtracts 1 more. The right side gains 1 from a bigger starting number but loses in the subtraction because it subtracts less. This creates a net gain of 2 for the right side. Therefore 213 - 77 < 214 - 76.
In simple words: The right side starts 1 higher and also takes away 1 less, so it ends up 2 more than the left side.

Exam Tip: Track changes from both parts - the starting number and the amount subtracted - to find the net difference.

Question 15. Mallesh brought 30 marbles to the playground. Arun brought 5 bags of marbles with 4 marbles in each bag. How many marbles did Mallesh and Arun bring to the playground? Mallesh summarized this by writing the mathematical expression - 30 + 5 x 4. Mallesh evaluated it as 30+(5×4) = 50. But why did Purna get it wrong?
Answer: The expression 30 + 5 x 4 written without brackets is unclear. It could mean either (30 + 5) × 4 = 140 or 30 + (5 × 4) = 50. Purna probably calculated it as the first way without knowing the context. Mallesh was right because he knew from the story that Arun brought 5 bags of 4 marbles each, so he should multiply 5 and 4 first before adding Mallesh's 30. Purna didn't have this context, so she didn't know which operation to do first. Without brackets to show the order clearly, different people can interpret the same expression in different ways and get different answers.
In simple words: Without brackets, people don't know whether to multiply first or add first. Brackets tell you which operation to do first.

Exam Tip: Always use brackets when writing expressions to make it clear which operation should be done first. Never leave an expression ambiguous.

Question 16. How are brackets used to clarify the order of operations in the expression 30 + 5 x 4 for the marbles example?
Answer: To show that we must first multiply Arun's bags by the marbles in each bag, we write brackets around that part: 30 + (5 x 4). By doing this, we tell the reader to calculate 5 x 4 first, getting 20. Then add 30 to get 50. The brackets act like an instruction saying "do this part first." Without brackets, it is unclear whether to add or multiply first, leading to confusion. With brackets, the order is unmistakable.
In simple words: Brackets show which part to calculate first. Anything inside brackets must be worked out before you add or subtract it.

Exam Tip: When writing an expression from a word problem, use brackets to show which part should be calculated first. This prevents confusion.

Question 17. Irfan bought a pack of biscuits for ₹15 and a packet of toor dal for ₹56. He gave the shopkeeper ₹100. Write an expression that can help us calculate the change Irfan will get back from the shopkeeper.
Answer: First find the total cost by adding the two items: 15 + 56 = 71. Then subtract this total from the money Irfan gave: 100 - 71 = 29. To make sure the addition happens first, use brackets: 100 - (15 + 56). Calculate inside the brackets first to get 71, then subtract from 100 to get 29. So Irfan will receive ₹29 in change.
In simple words: Add up what you're buying. Then subtract that from the money you gave. Use brackets to show you add first.

Exam Tip: When calculating change, always add the total cost first, then subtract from the amount given. Use brackets to show this clearly.

Question 18. Why is the expression 100 - 15 + 56 incorrect for calculating Irfan's change?
Answer: If you calculate 100 - 15 + 56 from left to right, you get: first subtract 15 to get 85, then add 56 to get 141. This gives an answer of ₹141, which doesn't make sense because Irfan only gave ₹100! The problem is that this expression subtracts only the biscuit cost, then adds the dal cost back in. What we really need is to subtract the total of both items. The correct expression must be 100 - (15 + 56), which ensures we subtract the complete total cost, not just part of it.
In simple words: The expression 100 - 15 + 56 doesn't subtract the total correctly. It would give an answer bigger than 100, which is impossible as change.

Exam Tip: Check if your answer makes sense in the real world. Change should never be more than the money you gave.

Question 19. Explain: Terms are parts separated by '+'. Subtraction is converted to adding the inverse (e.g., 83 - 14 becomes (83) + (-14)). Check if replacing subtraction by addition in this way does not change the value of the expression, by taking different examples.
Answer: Terms are pieces of an expression that are added together. Subtraction can be rewritten as adding a negative number. For example:

Example 1: 10 - 3 = 7. Also, 10 + (-3) = 7.
Example 2: 5 - 8 = -3. Also, 5 + (-8) = -3.
Example 3: -2 - 4 = -6. Also, -2 + (-4) = -6.

In each case, subtracting a number gives the same result as adding the negative version of that number. This method is useful because it lets us treat subtraction the same as addition, which makes it easier to rearrange the terms in an expression.
In simple words: Taking away 3 is the same as adding negative 3. Both give you the same answer.

Exam Tip: Remember that subtraction and adding negatives are equivalent. Use whichever method is easier for the problem you're solving.

Question 20. Can you explain why subtracting a number is the same as adding its inverse, using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Answer: In the Token Model, we represent numbers using positive and negative tokens. Subtracting a positive number means removing positive tokens from our collection. Adding a negative number means putting negative tokens into our collection. These negative tokens pair up with and cancel out positive tokens (creating zero pairs), which has the same effect as removing positive tokens. So removing 3 positive tokens is the same as adding 3 negative tokens - both result in losing 3 from your total. This is why subtracting a number gives the same result as adding the opposite number.
In simple words: Removing 3 tokens is the same as adding 3 negative tokens because the negative tokens cancel out the positive ones.

Exam Tip: Use the token model to understand why subtraction and adding opposites work the same way. This helps you solve problems with negative numbers.

Question 21. Complete the table (identifying terms). Expression: 5 + 6 x 3. Write it as a sum of terms and identify the terms.
Answer: The terms in this expression are the parts separated by '+'. First, evaluate any multiplication within each term, then separate. Expression as sum of terms: (5) + (6 x 3). The terms are: 5 and (6 x 3).
In simple words: Find the + sign. It separates the terms. Work out any multiplication inside each term first.

Exam Tip: Identify the main + or - signs first. These separate the terms. Only then evaluate what's inside each term.

Question 22. Expression: 4 + 15 - 9. Write it as a sum of terms and identify the terms.
Answer: Convert subtraction to adding the opposite: 4 + 15 - 9 becomes (4) + (15) + (-9). The terms are: 4, 15, and -9.
In simple words: Change all minus signs to plus signs with a negative number. Then the terms are all the separate pieces.

Exam Tip: Always rewrite subtraction as adding a negative. This makes it easier to identify and work with all the terms.

Question 23. Expression: 23 - 2 x 4 + 16. Write it as a sum of terms and identify the terms.
Answer: First identify the main addition and subtraction signs (these separate terms). Then evaluate any multiplication or division within a term. The expression becomes: (23) + (-2 x 4) + (16). The terms are: 23, (-2 x 4), and 16.
In simple words: Find where the plus and minus signs are - those separate the terms. Then solve any multiplication inside each term.

Exam Tip: Multiplication and division stay together as one term. They are not separated by + and - signs.

Question 24. Expression: 28 + 19 - 8. Write it as a sum of terms and identify the terms.
Answer: Convert subtraction by writing it as addition of a negative: (28) + (19) + (-8). The terms are: 28, 19, and -8.
In simple words: Turn the minus into a plus by using negative numbers. The terms are now all the pieces you're adding.

Exam Tip: Converting subtraction to adding negatives is a key skill. Practice this until it becomes automatic.

Question 25. Does changing the order in which the terms are added give different values?
Answer: No, changing the order of the terms does not change the final value. This is because addition of integers follows the commutative and associative properties. The commutative property says that a + b = b + a (order doesn't matter). The associative property says that (a + b) + c = a + (b + c) (grouping doesn't matter). These properties apply to both positive and negative numbers, so you can rearrange the terms of an expression in any order and still get the same answer.
In simple words: It doesn't matter what order you add the pieces in - you always get the same answer.

Exam Tip: Use the commutative and associative properties to rearrange terms in ways that make calculation easier.

Question 26. Madhu is flying a drone from a terrace. The drone goes 6 m up and then 4 m down. Write an expression to show how high the final position of the drone is from the terrace. Will the sum change if we swap the terms?
Answer: An up movement can be written as positive, and down as negative. The expression is 6 - 4, which as a sum of terms is (6) + (-4). This equals 2 m above the terrace. If we swap the terms, we get (-4) + (6), which also equals 2 m. So swapping the terms does not change the sum. The drone ends up 2 m above the terrace regardless of the order we write it in.
In simple words: Whether you go up 6 then down 4, or you write it as down 4 then up 6, you end up 2 m above where you started.

Exam Tip: The commutative property works even with negative numbers and mixed operations.

Question 27. Will this (swapping terms does not change the sum) also hold when there are terms having negative numbers as well? Take some more expressions and check.
Answer: Yes, swapping terms works even when all terms are negative numbers. Here are examples:

Example 1: (-5) + 8 = 3. Swapped: 8 + (-5) = 3. Same value.
Example 2: (-2) + (-7) = -9. Swapped: (-7) + (-2) = -9. Same value.

Because addition of integers is commutative, you can swap any terms in any order and get the same result. This is true whether the terms are positive, negative, or mixed.
In simple words: No matter what signs the numbers have, changing their order doesn't change the sum.

Exam Tip: Remember that the commutative property applies to all integers, positive or negative.

Question 28. Can you explain why this (swapping terms does not change the sum) is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Answer: Using the Token Model, addition means combining two or more collections of tokens. Whether you combine collection A with collection B, or collection B with collection A, the final pile of tokens stays exactly the same. You end up with the same number of positive and negative tokens either way. This demonstrates the commutative property - the order in which you combine the collections does not affect the final total. So swapping terms in an addition always gives the same answer.
In simple words: If you put pile A and pile B together, you get the same final pile no matter which pile you started with.

Exam Tip: The token model helps you visualize why rearranging terms doesn't change the answer.

Question 29. In an expression having two terms, show that swapping them does not change the value. (Term 1) + (Term 2) = (Term 2) + (Term 1)
Answer: This is the commutative property of addition. No matter what values the two terms have (whether positive, negative, fractions, or whole numbers), adding them in one order gives the same result as adding them in the opposite order. For example: (5) + (3) = 8 and (3) + (5) = 8. Also: (-7) + (10) = 3 and (10) + (-7) = 3. The left side and right side always equal the same value, proving the property holds.
In simple words: First term plus second term always equals second term plus first term.

Exam Tip: Use the commutative property to rearrange terms in ways that make your calculation simpler.

Question 30. Consider the expression (-7) + 10 + (-11). Demonstrate that grouping the terms differently does not change the sum.
Answer: Start by grouping and adding the first two terms, then the third:
((-7) + 10) + (-11) = (3) + (-11) = -8.

Now group differently by adding the last two terms first, then the first:
(-7) + (10 + (-11)) = (-7) + (-1) = -8.

Both groupings give the same answer of -8. This shows the associative property: the way you group the terms doesn't affect the final value, even with negative numbers.
In simple words: You can add the first two numbers first or the last two numbers first - either way, you get the same total.

Exam Tip: Use the associative property to group terms strategically - sometimes grouping certain terms first makes the calculation easier.

Question 31. Will this (grouping terms differently does not change the sum) also hold when there are terms having negative numbers as well? Take some more expressions and check.
Answer: Yes, grouping differently works even with all negative numbers. Here is an example:

(5 + (-3)) + (-4) = (2) + (-4) = -2

And:

5 + ((-3) + (-4)) = 5 + (-7) = -2

Both groupings produce the same answer of -2. This is the associative property of addition for integers. It works regardless of whether the terms are positive, negative, or a mix of both.
In simple words: No matter how you group the numbers, you always get the same answer.

Exam Tip: The associative property lets you group terms in ways that help you spot easy calculations.

Question 32. Can you explain why this (grouping does not change the sum) is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Answer: In the Token Model, adding three or more collections of tokens ultimately means putting all of them together into one large pile. It doesn't matter if you combine pile A and pile B first and then add pile C, or if you combine pile B and pile C first and then add pile A. The final combined pile will always contain the same total count of positive and negative tokens. The intermediate grouping steps don't affect the final result because the tokens don't change - only the order in which you combine them changes.
In simple words: If you combine piles of tokens in different orders, you always end up with the same total number of tokens.

Exam Tip: The token model shows why rearranging the order of operations in addition doesn't matter - the final total stays the same.

Question 33. Consider the expression (-7) + 10 + (-11) again. What happens when we change the order and add -7 and -11 first, and then add this sum to 10? Will we get the same sum as before?
Answer: Yes, we get the same sum. First add -7 and -11:
(-7) + (-11) = -18

Then add this sum to 10:
(-18) + 10 = -8

This equals -8, which is the same result obtained by all the other grouping methods shown earlier. This confirms that addition is associative - no matter which terms you group and add first, the final answer is always the same.
In simple words: Even when you add the two negative numbers first, you still get -8 at the end.

Exam Tip: Try different grouping orders for the same expression to build confidence in the associative property.

Question 34. Does adding the terms of an expression in any order give the same value? Take some more expressions and check. Consider expressions with more than 3 terms also.
Answer: Yes, adding the terms in any order gives the same value, even with more than 3 terms. Here is an example with 4 terms:

Original order: 10 + (-5) + 2 + (-3) = 5 + 2 + (-3) = 7 + (-3) = 4

Rearranged order: 10 + 2 + (-5) + (-3) = 12 + (-5) + (-3) = 7 + (-3) = 4

Both give the same result of 4. This is because addition follows both the commutative property (order of terms doesn't matter) and the associative property (grouping doesn't matter), and these work together to ensure that no matter how many terms you have or in what order you add them, you always get the same answer.
In simple words: Whether you have 2 terms or 10 terms, you can add them in any order and get the same total.

Exam Tip: Rearrange terms to group easy calculations together - this saves time without changing the answer.

Question 35. Can you explain why this (addition in any order gives same value) is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Answer: Using the Token Model, adding multiple terms means taking several collections of positive and negative tokens and combining them all into one large final pile. The final result depends only on the total count of positive and negative tokens across all the original collections - it does not depend on the sequence in which you combine the collections. Whether you combine collections in order A-B-C-D or in order D-C-B-A or any other sequence, you will always end up with the same final pile containing the same composition of tokens and representing the same value.
In simple words: The final pile of tokens is always the same no matter what order you combined the smaller piles in.

Exam Tip: Understanding the token model gives you a mental picture for why these properties work with addition.

Question 36. Evaluate the expression 30 + 5 x 4. Identify the terms and evaluate each term.
Answer: First identify the terms by looking for + and - signs that separate them. This expression has two terms: (30) and (5 x 4). Now evaluate each term: 30 remains 30, and 5 x 4 equals 20. Finally, add the evaluated terms: 30 + 20 = 50.
In simple words: The plus sign separates the two terms. Multiply 5 by 4 first to get 20. Then add 20 to 30.

Exam Tip: Always identify and evaluate the individual terms before adding or subtracting them together.

Question 37. Evaluate the expression 5 x (3 + 2) + 7 x 8 + 3. Identify the terms and evaluate each term.
Answer: First identify the terms by finding the main + signs: (5 x (3 + 2)), (7 x 8), and (3). Now evaluate each term:

Term 1: 5 x (3 + 2) = 5 x 5 = 25
Term 2: 7 x 8 = 56
Term 3: 3

Finally add all evaluated terms: 25 + 56 + 3 = 81 + 3 = 84.
In simple words: Work out the brackets first. Then multiply or divide inside each term. Then add all the answers together.

Exam Tip: The plus signs at the main level separate the terms - don't confuse them with plus signs inside brackets.

Question 38. Manasa is adding a long list of numbers. It took her five minutes to add them all and she got the answer 11749. Then she realised that she had forgotten to include the fourth number 9055. Does she have to start all over again?
Answer: No, she does not need to start from the beginning. Because addition is commutative and associative, she can simply add the forgotten number to her previous sum. She can calculate: 11749 + 9055 = 20804. This is much faster than redoing all the original calculations. The commutative and associative properties tell us that the order and grouping of terms don't matter, so adding the missed number to the final result gives the correct total.
In simple words: Add the number you forgot to your answer instead of starting over.

Exam Tip: Use the commutative and associative properties to save time - if you've already calculated part of the answer, you can add the missing parts later.

Question 39. Manasa is going outside to play. Her mother says, "Wear your hat and shoes!" Which one should she wear first?
Answer: It doesn't matter which she wears first. Whether she puts on the hat and then shoes, or shoes and then hat, she ends up in the same final state - wearing both items. This situation is commutative, just like addition. However, not all sequences are commutative in real life. For example, wearing socks before shoes is not the same as wearing shoes before socks - the order matters there because of the physical constraints. In mathematics, addition is always commutative, but other operations sometimes are not.
In simple words: Hat then shoes is the same as shoes then hat, but socks must come before shoes.

Exam Tip: Commutative means the order doesn't affect the result. Not all operations in math or life are commutative.

Question 40. Amu, Charan, Madhu, and John (4 people) went to a hotel and ordered four dosas. Each dosa cost ₹23 and they wish to thank the waiter by tipping ₹5. Write an expression describing the total cost.
Answer: The cost of 4 dosas at ₹23 each is 4 x 23 = 92. Adding the tip of ₹5 gives: (4 x 23) + 5. This evaluates to 92 + 5 = 97. So the total cost is ₹97.
In simple words: Multiply the number of dosas by the cost of each one. Then add the tip to get the total.

Exam Tip: Break the problem into parts (food cost, then tip). Write brackets to show which operations happen first.

Question 41. If the total number of friends goes up to 7 (ordering 7 dosas at ₹23 each) and the tip remains the same (₹5), how much will they have to pay? Write an expression for this situation and identify its terms.
Answer: The cost of 7 dosas at ₹23 each is 7 x 23. Adding the same tip of ₹5 gives the expression: (7 x 23) + 5. The terms are (7 x 23) and 5. Evaluating: 7 x 23 = 161, so 161 + 5 = 166. They will have to pay ₹166.
In simple words: Multiply 7 by 23 to get the food cost. Add 5 for the tip. That's your total.

Exam Tip: When a situation changes slightly (more people, same tip), adjust only the relevant number in your expression.

Question 42. Children playing "Fire in the mountain". 33 students playing, Ruby sitting out. Teacher calls out '5'. Students form groups of 5. Ruby wrote 6 x 5 + 3. Think and discuss why she wrote this.
Answer: When 33 students try to form groups of 5, Ruby divides: 33 divided by 5 gives 6 groups with 3 students remaining (because 33 = 6 x 5 + 3). Her expression shows 6 complete groups of 5 students each (6 x 5 = 30), plus the 3 students left over who couldn't form a full group. This total equals 30 + 3 = 33 students, matching the original count. Ruby's expression correctly represents the grouping situation - the multiplication part counts the complete groups, and the addition part accounts for the students who didn't fit into a group.
In simple words: 6 complete groups of 5 students make 30. The extra 3 students who are left out makes it 33 total.

Exam Tip: Division with a remainder can be written as a multiplication expression. This is useful for solving problems about grouping.

Question 43. How is the expression 6 x 5 + 3 written as a sum of terms?
Answer: Terms are separated by '+' and '-' signs. Multiplication is evaluated first within each term. The expression 6 x 5 + 3 written as a sum of terms is (6 x 5) + (3). The two terms are (6 x 5) and 3. Evaluating the first term: 6 x 5 = 30, so the expression equals 30 + 3 = 33.
In simple words: The plus sign separates the terms. Multiply first inside the first term, then add.

Exam Tip: Write each term in brackets to make it clear which operations belong to which term.

Question 44. If the teacher had called out '4': What expression represents the groups?
Answer: Dividing 33 students into groups of 4: 33 / 4 = 8 with a remainder of 1 (because 33 = 8 x 4 + 1). The expression is 8 x 4 + 1, with terms (8 x 4) and 1. This equals 32 + 1 = 33 students.
In simple words: Eight groups of 4 students make 32. One student is left alone, making 33 total.

Exam Tip: Each group size produces a different quotient and remainder, so write a new expression each time.

Question 45. If the teacher had called out '7': What expression represents the groups?
Answer: Dividing 33 students into groups of 7: 33 / 7 = 4 with a remainder of 5 (because 33 = 4 x 7 + 5). The expression is 4 x 7 + 5, with terms (4 x 7) and 5. This equals 28 + 5 = 33 students.
In simple words: Four groups of 7 students make 28. Five students are left alone, making 33 total.

Exam Tip: Use division to find how many complete groups you can make. The remainder becomes the second term.

Question 46. Raghu bought 100 kg of rice from the wholesale market and packed them into 2 kg packets. He already had four 2 kg packets. Write an expression for the number of 2 kg packets of rice he has now and identify the terms.
Answer: First find how many packets he made from 100 kg: 100 / 2 = 50 new packets. He already had 4 packets. So the total expression is: 4 + (100 / 2). The terms are 4 and (100/2). The total value is 4 + 50 = 54 packets.
In simple words: Divide 100 kg by 2 kg per packet to get 50 new packets. Add the 4 old packets to get 54 total.

Exam Tip: When combining old and new quantities, make sure each term is clearly identified with brackets.

Question 47. Kannan has to pay ₹432 using coins of ₹1 and ₹5, and notes of ₹10, ₹20, ₹50 and ₹100. Two ways are shown: Way 1: 4 x 100 + 1 x 20 + 1 x 10 + 2 x 1. Way 2: 8 x 50 + 1 x 10 + 4 x 5 + 2 x 1. Identify the terms in the two expressions above.
Answer: Terms in Way 1: (4 x 100), (1 x 20), (1 x 10), (2 x 1).

Terms in Way 2: (8 x 50), (1 x 10), (4 x 5), (2 x 1).

Each term represents a denomination (coin or note value) multiplied by how many of that denomination are used. All terms are separated by + signs.
In simple words: Each term shows one type of coin or note times how many of that type you need.

Exam Tip: When listing terms in expressions with multiple multiplications and additions, wrap each term in brackets for clarity.

Question 48. Can you think of some more ways of giving ₹432 to someone?
Answer: Yes, there are many ways to make ₹432. Here are two more examples:

Way 3: 3 notes of ₹100, 6 notes of ₹20, 1 note of ₹10, 2 coins of ₹1.
Expression: 3 x 100 + 6 x 20 + 1 x 10 + 2 x 1 = 300 + 120 + 10 + 2 = 432

Way 4: 20 notes of ₹20, 1 note of ₹10, 2 coins of ₹1 (Note: This is actually 20 x 20 + 1 x 10 + 2 x 1 = 400 + 10 + 2 = 412, which is only 412, so here's a corrected version):
Way 4 (corrected): 4 notes of ₹100, 3 notes of ₹10, 2 coins of ₹1.
Expression: 4 x 100 + 3 x 10 + 2 x 1 = 400 + 30 + 2 = 432
In simple words: Many combinations of coins and notes can add up to 432. Mix large denominations with smaller ones in different ways.

Exam Tip: For currency problems, start with larger denominations first. This reduces the remaining amount and makes finding combinations easier.

Question 49. Here are two pictures (arrangements of squares). Which of these two arrangements matches with the expression 5 x 2 + 3?
Answer: The expression 5 x 2 + 3, written as a sum of terms, is (5 x 2) + (3). This means "3 more than (5 multiplied by 2)". So you start with 2 groups of 5 squares (which is 10 squares), and then add 3 more separate squares. This matches the arrangement on the left, which visually shows two groups of 5 squares plus 3 additional individual squares arranged separately.
In simple words: First count 5 squares twice (10 total). Then add 3 more squares. That's 13 squares altogether.

Exam Tip: Draw or visualize the arrangement as you interpret the expression. Multiplication creates groups, addition adds singles.

Question 50. What is the expression for the arrangement in the right making use of the number of yellow and blue squares?
Answer: The arrangement on the right shows 2 rows. Each row has 5 yellow squares and 3 blue squares (8 squares per row). Possible expressions for this are:

1. 2 x (5 + 3) - meaning 2 times the sum of 5 and 3
2. 5 + 3 + 5 + 3 - meaning the squares in row 1 plus the squares in row 2
3. 5 x 2 + 3 x 2 - meaning (all yellow squares) plus (all blue squares)

All three evaluate to 16. The expression 2 x (5 + 3) uses brackets to show you add the yellow and blue first (within each row), then multiply by 2 for the two rows.
In simple words: You can group the squares by rows, or by colors, or by counting the same row twice. Each method gives 16.

Exam Tip: Different expressions can represent the same picture. Show flexibility by finding multiple valid expressions.

Question 51. Write the following expressions as a sum of terms and identify the terms in each case. (a) 28 - 7 + 8
Answer: Convert subtraction to adding the opposite: (28) + (-7) + (8). The terms are: 28, -7, and 8.
In simple words: The minus sign becomes a plus sign with a negative number.

Exam Tip: Always rewrite subtraction as addition of negatives when identifying terms.

Question 52. (b) 5 x 12 - 6
Answer: Write as a sum of terms: (5 x 12) + (-6). The terms are: (5 x 12) and -6. Note that multiplication happens first within the first term, so the term is the whole product (5 x 12), not just 5 or just 12.
In simple words: Multiply 5 by 12 first. That's one term. The second term is negative 6.

Exam Tip: Operations like multiplication that happen within a term stay grouped together in brackets.

Question 53. (c) 40 - 10 + 10 + 10
Answer: Write as a sum of terms: (40) + (-10) + (10) + (10). The terms are: 40, -10, 10, and 10.
In simple words: Change the minus sign to a plus with negative 10. Now you have four terms to add.

Exam Tip: Even when a number appears multiple times, it's still separate terms if it's not being multiplied or grouped together.

Question 54. (d) 39 - 2 x 6 + 11
Answer: The main + and - signs separate the terms. Convert subtraction: (39) + (-2 x 6) + (11). The terms are: 39, (-2 x 6), and 11. Note that 2 x 6 stays together as one term because multiplication is part of that term.
In simple words: The first term is 39. The second term is negative 2 times 6. The third term is 11.

Exam Tip: Don't break apart products when identifying terms. The multiplication operation belongs entirely to one term.

Question 55. (e) 6 x 3 - 4 x 8 x 5
Answer: Write as a sum of terms: (6 x 3) + (-4 x 8 x 5). The terms are: (6 x 3) and (-4 x 8 x 5). Note that the second term is a product of three factors: -4, 8, and 5.
In simple words: The first term is 6 times 3. The second term is the negative of (4 times 8 times 5).

Exam Tip: When subtraction precedes a product, the entire product becomes negative. Keep all factors together.

Question 56. (f) 48 - 10 x 2 + 16 / 2
Answer: Write as a sum of terms: (48) + (-10 x 2) + (16 / 2). The terms are: 48, (-10 x 2), and (16/2). Multiplication and division within each term stay grouped together.
In simple words: The first term is just 48. The second term is negative 10 times 2. The third term is 16 divided by 2.

Exam Tip: Division within a term stays grouped just like multiplication does.

Question 57. Find the values of the expressions identified in the above questions. (a) 28 - 7 + 8
Answer: Calculate from left to right: 28 - 7 = 21. Then 21 + 8 = 29. The value is 29.
In simple words: Subtract 7 from 28, then add 8 to the answer.

Exam Tip: For expressions with only addition and subtraction, work from left to right.

Question 58. (b) 5 x 12 - 6
Answer: Multiplication happens before subtraction. Calculate 5 x 12 = 60. Then subtract 6: 60 - 6 = 54. The value is 54.
In simple words: Multiply first to get 60. Then take away 6.

Exam Tip: Always do multiplication and division before addition and subtraction.

Question 59. (c) 40 - 10 + 10 + 10
Answer: Work left to right: 40 - 10 = 30. Then 30 + 10 = 40. Then 40 + 10 = 50. The value is 50.
In simple words: Subtract 10, then add 10 twice.

Exam Tip: When operations have the same priority, go left to right.

Question 60. (d) 39 - 2 x 6 + 11
Answer: First do multiplication: 2 x 6 = 12. The expression becomes: 39 - 12 + 11. Now work left to right: 39 - 12 = 27. Then 27 + 11 = 38. The value is 38.
In simple words: Multiply 2 by 6 to get 12. Then subtract from 39 to get 27. Then add 11.

Exam Tip: Do all multiplications and divisions first, then handle addition and subtraction from left to right.

Question 61. (e) 6 x 3 - 4 x 8 x 5
Answer: Do all multiplications first: 6 x 3 = 18 and 4 x 8 x 5 = 32 x 5 = 160. Now subtract: 18 - 160 = -142. The value is -142.
In simple words: Work out both products. Then subtract the second from the first.

Exam Tip: When subtracting a large number from a small number, you get a negative answer.

Question 62. (f) 48 - 10 x 2 + 16 / 2
Answer: First do multiplication and division: 10 x 2 = 20 and 16 / 2 = 8. The expression becomes: 48 - 20 + 8. Now work left to right: 48 - 20 = 28. Then 28 + 8 = 36. The value is 36.
In simple words: Multiply and divide first. Then subtract and add from left to right.

Exam Tip: Multiplication and division have the same priority. Do whichever comes first from left to right.

Question 63. For each situation, write the expression, identify terms, and find the value. (a) Queen Alia gave 100 coins each to Elsa and Anna. Elsa doubled hers (2×100). Anna has half left (100/2). How many together?
Answer: Elsa's total: 2 x 100 = 200 coins. Anna's total: 100 / 2 = 50 coins. The expression for the total is: (2 x 100) + (100 / 2). The terms are: (2 x 100) and (100 / 2). Finding the value: 200 + 50 = 250 coins altogether.
In simple words: Elsa doubles her coins. Anna cuts hers in half. Add both amounts.

Exam Tip: Identify what each person has. Then write it as an expression with clear terms for each person.

Question 64. (b) Metro: Adult=₹40, Child=₹20. Total cost for: (i) four adults and three children?
Answer: Cost for 4 adults: 4 x 40 = 160. Cost for 3 children: 3 x 20 = 60. The expression is: (4 x 40) + (3 x 20). The terms are: (4 x 40) and (3 x 20). Total cost: 160 + 60 = ₹220.
In simple words: Multiply adults by 40. Multiply children by 20. Add both costs.

Exam Tip: Make separate terms for each category (adults and children). Then add them together.

Question 65. (ii) for two groups having three adults each?
Answer: Two groups with 3 adults each means 2 x (3 x 40) or (2 x 3) x 40 = 6 x 40. The expression is: 2 x (3 x 40). Without calculating fully, this can also be written as 6 x 40 = 240 using the associative property of multiplication.
In simple words: Two groups of three adults each is the same as 6 adults total. Multiply 6 by 40.

Exam Tip: Recognize that 2 x (3 x 40) and (2 x 3) x 40 are the same due to the associative property.

Question 66. (c): Find the total height of the window by writing an expression describing the relationship among the measurements shown in the picture. Identify its terms and find the value.
Answer: The window consists of:
- Top Border: 3 cm
- First Grill: 12 cm
- First Gap: 5 cm
- Second Grill: 12 cm
- Second Gap: 5 cm
- Third Grill: 12 cm
- Bottom Border: 3 cm

Expression for total height: 3 + 12 + 5 + 12 + 5 + 12 + 3

Alternatively, grouping similar parts: (2 x 3) + (3 x 12) + (2 x 5)

Terms (based on grouped expression): (2 x 3), (3 x 12), (2 x 5)

Value Calculation: 6 + 36 + 10 = 52 cm. The total height of the window is 52 cm.
In simple words: Add up all the pieces. You can group the same sizes together to make calculation easier.

Exam Tip: For complex measurements, group identical parts together using multiplication. This makes the expression simpler.

Question 67. Evaluating 200 - (40 + 3): Show both methods - using brackets first, and removing brackets.
Answer: Method 1 (Brackets first): Calculate inside brackets: 40 + 3 = 43. Then subtract from 200: 200 - 43 = 157.

Method 2 (Removing brackets): When removing brackets preceded by '-', change the sign of each term inside. So 200 - (40 + 3) becomes 200 - 40 - 3. Calculate left to right: 200 - 40 = 160. Then 160 - 3 = 157.

Both methods give the same answer: 157. The key observation is that 200 - (40 + 3) = 200 - 40 - 3.
In simple words: You can calculate inside brackets first, or you can flip the signs and remove the brackets. Either way, you get the same answer.

Exam Tip: Learn to remove brackets with a minus sign in front. This skill saves time on longer expressions.

Question 68. Calculating 100 - (15 + 56): Demonstrate both methods and explain how they're equivalent.
Answer: Method 1 (Brackets first): Calculate inside brackets: 15 + 56 = 71. Then subtract: 100 - 71 = 29.

Method 2 (Step-by-step subtraction): Subtract the first item (100 - 15 = 85), then subtract the second item (85 - 56 = 29). This sequence is 100 - 15 - 56.

The key observation: 100 - (15 + 56) = 100 - 15 - 56. When you remove brackets preceded by a minus sign, change each plus inside to a minus. The final answer is 29 in both cases.
In simple words: Subtracting a sum is the same as subtracting each item one by one.

Exam Tip: Removing brackets with a minus sign means flipping all the signs inside. A plus becomes minus, and a minus becomes plus.

Question 69. Consider the expression 500 - (250 - 100). Is it possible to write this expression without the brackets?
Answer: Yes, it is possible. First, let's calculate with brackets: inside brackets, 250 - 100 = 150. Then 500 - 150 = 350.

When removing brackets preceded by '-': change the sign of each term inside. The expression 500 - (250 - 100) becomes 500 - 250 + 100. Calculate: 500 - 250 = 250. Then 250 + 100 = 350.

Both methods give 350. Note that 500 - 250 + 100 is NOT the same as 500 - 250 - 100 (which would equal 150). The rule is crucial: when removing brackets preceded by a minus sign, +250 becomes -250, and -100 becomes +100.
In simple words: The minus sign in front of the brackets flips all the signs inside. Plus becomes minus, and minus becomes plus.

Exam Tip: This is a tricky rule. Practice it several times until flipping signs inside brackets becomes automatic.

Question 70. Hira has 28 coins in one bag and 35 in another. She gifts 10 coins from the second bag. Write an expression for the number of coins left with Hira.
Answer: Coins left = Coins in bag 1 + (Coins in bag 2 - Gifted coins). So the expression is: 28 + (35 - 10). When removing brackets not preceded by '-' (here it's preceded by '+'), the signs inside do not change. The equivalent expression is: 28 + 35 - 10. Calculate: 28 + 25 = 53 (evaluating what's in brackets first), or 28 + 35 - 10 = 63 - 10 = 53. Hira has 53 coins left.
In simple words: She still has all the coins from the first bag. From the second bag, she loses 10 but keeps the rest.

Exam Tip: When brackets are preceded by a plus sign, you don't change the signs inside. Just remove the brackets.

Question 71. Given: 53 + (-16) = 37. Calculate: 54 + (-16) = ?
Answer: Since 54 is 1 more than 53, the sum will also be 1 more than 37. Therefore, 54 + (-16) = 38.
In simple words: If the first number gets 1 bigger, the total gets 1 bigger too.

Exam Tip: You don't always need to calculate fully. If one term changes by a certain amount, the total changes by the same amount.

Question 72. Given: 53 + (-16) = 37. Calculate: 52 + (-16) = ?
Answer: Since 52 is 1 less than 53, the sum will be 1 less than 37. Therefore, 52 + (-16) = 36.
In simple words: If the first number gets 1 smaller, the total gets 1 smaller too.

Exam Tip: Understanding how changes in one term affect the total helps you solve problems without recalculating everything.

Question 73. Given: 53 + (-16) = 37. Calculate: 53 + (-15) = ?
Answer: Since -15 is 1 more than -16 (it's closer to zero), the sum will be 1 more than 37. Therefore, 53 + (-15) = 38.
In simple words: If you add a number that's less negative, you add more, so the total goes up.

Exam Tip: When the second term becomes less negative (closer to zero), the total increases.

Question 74. Given: 53 + (-16) = 37. Calculate: 53 + (-17) = ?
Answer: Since -17 is 1 less than -16 (it's further from zero), the sum will be 1 less than 37. Therefore, 53 + (-17) = 36.
In simple words: If you add a number that's more negative, you take away more, so the total goes down.

Exam Tip: When the second term becomes more negative (further from zero), the total decreases.

Question 75. Given: -87 - 16 = -87 + (-16) = -103. Calculate: -88 + (-15) = ?
Answer: Compare to the given -87 + (-16) = -103. In the new expression -88 + (-15): the first term -88 is 1 less than -87 (moving further away from zero), and the second term -15 is 1 more than -16 (moving closer to zero). The first change decreases the total by 1, the second change increases the total by 1. These cancel out, so the answer is -103.
In simple words: One term gets 1 more negative (minus 1). The other term gets 1 less negative (plus 1). These changes cancel out.

Exam Tip: When changes in different terms work in opposite directions, they can cancel each other out.

Question 76. Given: -87 - 16 = -87 + (-16) = -103. Calculate: -86 + (-18) = ?
Answer: Compare to -87 + (-16) = -103. In the new expression -86 + (-18): the first term -86 is 1 more than -87 (moving closer to zero, which increases the total by 1), and the second term -18 is 2 less than -16 (moving further from zero, which decreases the total by 2). The net change is +1 - 2 = -1. Therefore, the total is -103 - 1 = -104.
In simple words: The first term gets 1 less negative (plus 1). The second term gets 2 more negative (minus 2). Together, that's a change of minus 1.

Exam Tip: Track changes in each term separately. Then combine these changes to find the net effect on the total.

Question 77. Fill in the blanks with numbers, and boxes with operation signs such that the expressions on both sides are equal. (a) 24 + (6 - 4) = 24 + 6 ___ 4
Answer: When removing brackets preceded by '+', the signs inside do not change. So 24 + (6 - 4) = 24 + 6 - 4. The operation sign to fill in is - (minus).
In simple words: The plus sign outside the brackets doesn't flip the signs inside.

Exam Tip: Removing brackets after a plus sign is simple - just remove the brackets and keep the signs as they are.

Question 78. (b) 38 + ( ___ ) = 38 + 9 - 4
Answer: The right side is 38 + 9 - 4 = 47 - 4 = 43. The left side is 38 + (___), which must also equal 43. So the blank must be 43 - 38 = 5. Therefore the answer is 5 (or it could be written as 9 - 4 if we want to show the bracket contents).
In simple words: Calculate the right side first. Then find what number you need to add to 38 to get that total.

Exam Tip: The blank inside brackets can be either a single number or an expression, depending on what the question wants.

Question 79. (c) 24 - (6 + 4) = 24 ___ 6 ___ 4
Answer: When removing brackets preceded by '-', change the sign of each term inside. So 24 - (6 + 4) becomes 24 - 6 - 4. The two operation signs are - and - (both minus).
In simple words: The minus sign in front flips the plus signs inside to minus signs.

Exam Tip: When removing brackets with a minus sign, always flip every sign inside.

Question 80. (d) 24 - 6 - 4 = 24 - 6 (__) ______
Answer: The left side equals 24 - 10 = 14. The right side must equal 14. We need to write this as 24 - (something). If we put it as 24 - (6 + 4), then removing brackets gives 24 - 6 - 4. So the blanks are: ( inside the parentheses, then + , then 4 ). Actually, rereading the question, it seems to ask for operation signs. So it would be: 24 - ( ) where the blank in brackets is 6 + 4, giving - and + as the operation signs. But following the literal format: 24 - 6 + 4 = 22, which is not 14. Let me recalculate. 24 - 6 - 4 = 14. If we write 24 - (6 + 4) = 24 - 10 = 14. Removing the brackets: 24 - 6 - 4. So filling in the boxes: 24 - ( 6 + 4 ).
In simple words: Put brackets around the 6 + 4 and put a minus sign in front to get the original expression.

Exam Tip: Rewrite expressions with brackets by finding what goes inside and what sign comes before the brackets.

Question 81. (e) 27 - (8 + 3) = 27 ___ 8 ___ 3
Answer: When removing brackets preceded by '-', change the signs. So 27 - (8 + 3) becomes 27 - 8 - 3. The operation signs are - and - (both minus).
In simple words: Flip the plus inside to a minus when you remove the brackets.

Exam Tip: Practice the bracket-removal rule until it's automatic.

Question 82. (f) 27 - ( ___ ) = 27 - 8 + 3
Answer: The right side is 27 - 8 + 3 = 19 + 3 = 22. For the left side to equal 22, we need 27 - (___) = 22. So ___ = 27 - 22 = 5. The expression inside the brackets can be written as 5, or as the expression 8 - 3 (since 8 - 3 = 5).
In simple words: Calculate the right side. Then find what to subtract from 27 to get that total.

Exam Tip: Sometimes the blank can be filled with a single number or an expression - both are correct if they have the same value.

Question 83. Remove the brackets and write the expression having the same value. (a) 14 + (12 + 10)
Answer: Since the brackets are preceded by a '+', remove them without changing the signs inside: 14 + 12 + 10.
In simple words: Just take away the brackets. The plus sign outside doesn't change anything inside.

Exam Tip: Brackets preceded by plus are the easiest - just remove them and nothing else changes.

Question 84. (b) 14 - (12 + 10)
Answer: Since the brackets are preceded by '-', flip all the signs inside. The +12 becomes -12, and the +10 becomes -10. So: 14 - 12 - 10.
In simple words: The minus sign in front flips both plus signs inside.

Exam Tip: Always flip every sign when removing brackets preceded by a minus.

Question 85. (c) 14 + (12 - 10)
Answer: Since the brackets are preceded by '+', keep the signs as they are: 14 + 12 - 10.
In simple words: The plus outside doesn't change the minus inside.

Exam Tip: Plus always preserves the signs inside brackets.

Question 86. (d) 14 - (12 - 10)
Answer: Since the brackets are preceded by '-', flip all signs. The +12 (understood) becomes -12, and the -10 becomes +10. So: 14 - 12 + 10.
In simple words: The minus sign flips the minus inside into a plus.

Exam Tip: Minus flips every sign - plus becomes minus, minus becomes plus.

Question 87. (e) -14 + 12 - 10
Answer: There are no brackets to remove. The expression is already written without brackets: -14 + 12 - 10.
In simple words: This expression has no brackets, so there's nothing to remove.

Exam Tip: Check if brackets exist before trying to remove them.

Question 88. (f) 14 - (-12 - 10)
Answer: Since the brackets are preceded by '-', flip all signs. The -12 becomes +12, and the -10 becomes +10. So: 14 + 12 + 10.
In simple words: Both negative numbers inside become positive when the minus flips them.

Exam Tip: When flipping signs, minus becomes plus and plus becomes minus.

Question 89. Find the values of the following expressions. For each pair, first try to guess whether they have the same value. (a) (6 + 10) - 2 and 6 + (10 - 2)
Answer: Guess: These look like they might be equal due to the associative property, but addition and subtraction mixed can be tricky. Let me calculate:

(6 + 10) - 2 = 16 - 2 = 14
6 + (10 - 2) = 6 + 8 = 14

They are equal! This shows that associativity seems to hold when the operations are applied in this particular arrangement.
In simple words: Even though the brackets are in different places, you get the same answer.

Exam Tip: Make a guess, then check. Building intuition about when expressions are equal is valuable.

Question 90. (b) 16 - (8 - 3) and (16 - 8) - 3
Answer: Guess: These look different because of how the brackets are placed, so they might not be equal.

16 - (8 - 3) = 16 - 5 = 11
(16 - 8) - 3 = 8 - 3 = 5

They are not equal! This shows that subtraction is not associative - the position of the brackets matters significantly with subtraction.
In simple words: With subtraction, where you put the brackets changes the answer.

Exam Tip: Subtraction is not associative. Always be careful about bracket placement in subtraction problems.

Question 91. (c) 27 - (18 + 4) and 27 + (-18 - 4)
Answer: Guess: These look different but they might be connected by the bracket-removal rule.

27 - (18 + 4) = 27 - 22 = 5
27 + (-18 - 4) = 27 + (-22) = 5

They are equal! This shows that subtracting a sum is the same as adding the sum of the negatives (each term made negative).
In simple words: Subtracting a sum of numbers is the same as adding their negatives.

Exam Tip: This is a key property - it connects subtraction and addition through negative numbers.

Question 92. In each of the sets of expressions below, identify those that have the same value. Do not evaluate them, but rather use your understanding of terms. (a) 319 + 537, 319 - 537, 537 + 319, -537 + 319, 537 - 319
Answer: Group 1 (Equal): 319 + 537 and 537 + 319. These are equal because addition is commutative - the order doesn't matter.

Group 2 (Equal): 319 - 537 and -537 + 319. These are equal. The first one subtracts 537 from 319. The second adds -537 to 319. Subtraction and adding the opposite are the same.

Group 3 (Unique): 537 - 319. This is different from the others because it subtracts the smaller from the larger.
In simple words: Group expressions by whether they add the same numbers in the same way, even if written differently.

Exam Tip: Use properties like commutativity and the equivalence of subtraction to adding opposites to group expressions without calculating.

Question 93. (b) 87 + 46 - 109, -(46 + 109), 87 - (46 - 109), (87 - 46) + 109, 87 + (-46 - 109)
Answer: Let me first rewrite each expression to see the terms:

Expression 1: 87 + 46 - 109
Expression 2: -(46 + 109) = -46 - 109
Expression 3: 87 - (46 - 109) = 87 - 46 + 109 (removing the brackets by flipping signs)
Expression 4: (87 - 46) + 109 = 87 - 46 + 109
Expression 5: 87 + (-46 - 109) = 87 - 46 - 109

Groups with same value:
- Expressions 3 and 4 both equal 87 - 46 + 109
- Expression 1 (87 + 46 - 109) stands alone
- Expression 2 (-46 - 109) stands alone
- Expression 5 (87 - 46 - 109) stands alone
In simple words: Rewrite each expression by removing brackets, then compare which ones have the same terms.

Exam Tip: Always remove brackets first. Then comparing becomes much easier.

Question 5. Add brackets at appropriate places in the expressions such that they lead to the values indicated.
(a) 34 - 9 + 12 = 13
Answer: To achieve 34 - 9 + 12 = 13, place brackets as: 34 - (9 + 12). Work: 34 - (9 + 12) = 34 - 21 = 13.
In simple words: Put brackets around the 9 and 12 that are being added together, then subtract that sum from 34.

Exam Tip: Always check the order of operations - brackets force certain parts to be calculated first before others.

Question 5. (b) 56 - 14 - 8 = 34
Answer: Since the default direction is left-to-right, we get (56 - 14) - 8 = 42 - 8 = 34. No brackets are needed, or you can write them as: (56 - 14) - 8.
In simple words: When you subtract from left to right without brackets, you naturally get 34.

Exam Tip: Remember that subtraction works left-to-right unless brackets change the order.

Question 5. (c) -22 - 12 + 10 + 22 = -22
Answer: We need the last three terms to combine to zero when subtracted from -22. Notice that 12 + 10 - 22 = 0. So place brackets as: -22 - (12 + 10 - 22). This gives -22 - 0 = -22.
In simple words: The three numbers 12, 10, and 22 add and subtract to make zero, so putting brackets around them and subtracting that zero from -22 leaves us with -22.

Exam Tip: Look for combinations that sum to zero inside brackets - this simplifies the final answer.

Question 6. Using only reasoning of how terms change their values, fill the blanks to make the expressions on either side of the equality (=) equal.
(a) 423 + ___ = 419 + ___
Answer: Since 419 is 4 less than 423, to keep both sides equal, the second blank must be 4 more than the first blank. For example: 423 + 5 = 419 + 9, where 9 is 4 more than 5.
In simple words: The right side starts with a smaller number, so it needs to add a larger number to match the left side.

Exam Tip: Think about the difference between the first numbers - this tells you how much extra the second number must be.

Question 6. (b) 207 - 68 = 210 - ___
Answer: The first number on the right, 210, is 3 more than the first number on the left, 207. To maintain equality, we must subtract 3 more on the right than on the left. So subtract 68 + 3 = 71. Check: 207 - 68 = 139 and 210 - 71 = 139.
In simple words: The right side starts bigger by 3, so we need to take away 3 more to end up with the same answer.

Exam Tip: Always verify both sides give the same result after you fill in the blank.

Question 7. Using the numbers 2, 3 and 5, and the operators '+' and '-' and brackets, as necessary, generate expressions to give as many different values as possible.
Answer: Many different expressions can be formed. Here are examples:
2 + 3 + 5 = 10
5 + 3 - 2 = 6
3 - (2 - 5) = 3 - (-3) = 6
(5 - 2) + 3 = 3 + 3 = 6
2 - 3 + 5 = 4
5 + 2 - 3 = 4
2 - (3 - 5) = 2 - (-2) = 4
5 - (2 + 3) = 5 - 5 = 0
3 + 2 - 5 = 0
3 - (5 - 2) = 3 - 3 = 0
5 - 3 - 2 = 0
3 - 2 - 5 = -4
2 - (3 + 5) = 2 - 8 = -6
2 - 3 - 5 = -6
Different values obtained: 10, 6, 4, 0, -4, -6
In simple words: By arranging 2, 3, and 5 in different orders and adding or subtracting them with or without brackets, you can make at least six different final answers.

Exam Tip: Brackets change which numbers combine first, leading to completely different results - explore all bracket placements.

Question 8. Whenever Jasoda has to subtract 9 from a number, she subtracts 10 and adds 1 to it. For example, 36 - 9 = (36 - 10) + 1 = 26 + 1 = 27.
(a) Do you think she always gets the correct answer? Why?
Answer: Yes, she always gets the correct answer. This works because -9 is mathematically equal to -10 + 1. When you substitute (-10 + 1) in place of (-9) in any expression like N - 9, you get N + (-10 + 1), which simplifies to (N - 10) + 1 using the associative property.
In simple words: Subtracting 10 and adding 1 is the same as subtracting 9, because -10 + 1 = -9.

Exam Tip: Understanding equivalent operations helps create mental math shortcuts - look for how numbers can be rewritten.

Question 8. (b) Can you think of other similar strategies? Give some examples.
Answer: Yes, many similar tricks work:
- To subtract 8: Subtract 10, then add 2 (since -8 = -10 + 2). Example: 55 - 8 = (55 - 10) + 2 = 45 + 2 = 47.
- To subtract 19: Subtract 20, then add 1 (since -19 = -20 + 1). Example: 72 - 19 = (72 - 20) + 1 = 52 + 1 = 53.
- To add 9: Add 10, then subtract 1 (since +9 = +10 - 1). Example: 46 + 9 = (46 + 10) - 1 = 56 - 1 = 55.
- To add 98: Add 100, then subtract 2 (since +98 = +100 - 2). Example: 130 + 98 = (130 + 100) - 2 = 230 - 2 = 228.
In simple words: Find a nearby round number, do the operation with that, then adjust by the small difference to get your answer.

Exam Tip: These mental math tricks rely on breaking down numbers into easier parts - the key is recognizing the relationship between the number you want and a convenient round number.

Question 9. Consider the two expressions: a) 73 - 14 + 1, b) 73 - 14 - 1. For each of these expressions, identify the expressions from the following collection that are equal to it.
Options: (i) 73 - (14 + 1) (ii) 73 - (14 - 1) (iii) 73 + (-14 + 1) (iv) 73 + (-14 - 1)
Answer: For (a) 73 - 14 + 1: First evaluate: 73 - 14 + 1 = 59 + 1 = 60. Now check the options:
(i) 73 - (14 + 1) = 73 - 15 = 58. Does not match.
(ii) 73 - (14 - 1) = 73 - 13 = 60. Matches (a).
(iii) 73 + (-14 + 1) = 73 + (-13) = 60. Matches (a).
(iv) 73 + (-14 - 1) = 73 + (-15) = 58. Does not match.
For (b) 73 - 14 - 1: First evaluate: 73 - 14 - 1 = 59 - 1 = 58. Now check the options:
(i) 73 - (14 + 1) = 58. Matches (b).
(iv) 73 + (-14 - 1) = 58. Matches (b).
Equal to (a): (ii) and (iii).
Equal to (b): (i) and (iv).
In simple words: Work out what each expression equals, then check which options give the same answer.

Exam Tip: Brackets change which operations happen together - brackets around subtraction or addition change how terms combine.

Question. Why is the expression 2 x 43 + 24 incorrect for the total cost of two people each ordering a Rs 43 cutlet and a Rs 24 rasgulla?
Answer: When you evaluate 2 x 43 + 24 following order of operations, you get (2 x 43) + 24 = 86 + 24 = 110. This represents two cutlets plus only one rasgulla, which is wrong. For the correct answer, you must double the entire cost per person (43 + 24), not just the cutlet price.
In simple words: Without brackets, multiplication happens first, so 2 x 43 + 24 means "two cutlets plus one rasgulla," not "two of everything."

Exam Tip: Always use brackets when you want to multiply a total - brackets force the sum to be calculated before the multiplication.

Question. How are brackets used correctly for the hotel example and what property does it illustrate?
Answer: The correct expression is 2 x (43 + 24) = 2 x 67 = 134. The text also shows this is the same as (2 x 43) + (2 x 24) = 86 + 48 = 134. This demonstrates the distributive property: when you multiply a sum by a number, you get the same result as multiplying each part separately and then adding.
In simple words: Brackets let you multiply the whole group by 2, and it gives the same answer as multiplying each item by 2 and adding up the results.

Exam Tip: The distributive property is one of the most useful tools in algebra - recognizing when and how to apply it speeds up calculations greatly.

Question. If another friend, Sangmu, joins them (making 3 friends) and orders the same items (Rs 43 cutlet, Rs 24 rasgulla), what will be the expression for the total amount to be paid?
Answer: For 3 people, the cost per person is still 43 + 24. The total cost for 3 people is 3 x (43 + 24). Working it out: 3 x (43 + 24) = 3 x 67 = 201. Alternatively, using the distributive property: (3 x 43) + (3 x 24) = 129 + 72 = 201. The total cost is Rs 201.
In simple words: Multiply 3 by the cost of one person's meal to get what all three people pay together.

Exam Tip: When the problem scales up to more people or items, the same bracket method works - just change the multiplier.

Question. In the Republic Day parade, there are boy scouts (4 rows, 5 scouts/row) and girl guides (3 rows, 5 guides/row) marching together. How many scouts and guides are marching in this parade? (Two methods shown).
Answer: Method 1 (Calculate separately, then add):
- Number of scouts = 4 rows x 5 scouts/row = 20.
- Number of guides = 3 rows x 5 guides/row = 15.
- Total = 20 + 15 = 35 children.
- Expression: (4 x 5) + (3 x 5).

Method 2 (Combine rows first, then multiply):
- Total rows = 4 + 3 = 7 rows.
- Children per row = 5.
- Total = 7 x 5 = 35 children.
- Expression: (4 + 3) x 5.

Both methods give 35, showing that (4 x 5) + (3 x 5) = (4 + 3) x 5. This illustrates the distributive property.
In simple words: You can count scouts and guides separately and add them, or you can count total rows and multiply by children per row - both ways give the same answer.

Exam Tip: The distributive property works in both directions - you can expand or simplify depending on which method makes the calculation easier.

Question. Why is 5 x 4 + 3 ≠ 5 x (4 + 3)? Can you explain why?
Answer: Let's evaluate both sides:
- LHS: 5 x 4 + 3 = (5 x 4) + 3 = 20 + 3 = 23 (multiplication is done before addition).
- RHS: 5 x (4 + 3) = 5 x 7 = 35 (operation inside brackets is done first).
Since 23 ≠ 35, the expressions are not equal. The brackets change the order of operations - they force the 4 and 3 to be added first, then multiplied by 5, rather than multiplying 5 by 4 first and then adding 3.
In simple words: Brackets tell you which numbers go together - without brackets, multiplication happens before addition, so you get a different answer.

Exam Tip: Brackets have the power to completely change what a problem is asking - always respect the brackets.

Question. Is 5 x (4 + 3) = 5 x (3 + 4) = (3 + 4) x 5?
Answer: Yes, all three expressions are equal to 35.
- 5 x (4 + 3) = 5 x 7 = 35.
- 5 x (3 + 4) = 5 x 7 = 35 (because 4 + 3 = 3 + 4, showing the commutative property of addition).
- (3 + 4) x 5 = 7 x 5 = 35 (because 5 x 7 = 7 x 5, showing the commutative property of multiplication).
In simple words: You can rearrange the numbers being added or swap which number does the multiplying - the answer stays the same.

Exam Tip: The commutative properties let you rearrange terms to make a problem easier to solve mentally.

Question. Given 53 x 18 = 954. Find out 63 x 18.
Answer: Use the distributive property to relate the two problems. Since 63 = 53 + 10:
63 x 18 = (53 + 10) x 18
= (53 x 18) + (10 x 18)
= 954 + 180
= 1134
In simple words: Break 63 into 53 + 10, multiply each part by 18, then add the results. This lets you use the given answer of 53 x 18 = 954.

Exam Tip: When you see a given fact, look for how to rewrite the target problem using that fact - it saves calculation time.

Question. Find an effective way of evaluating 97 x 25. Find this value.
Answer: Write 97 as a difference from a round number: 97 = 100 - 3. Then:
97 x 25 = (100 - 3) x 25
= (100 x 25) - (3 x 25)
= 2500 - 75
= 2425
In simple words: Instead of multiplying 97 directly, multiply 100 by 25 (which is easy), multiply 3 by 25, and subtract the second result from the first.

Exam Tip: Look for numbers close to multiples of 10, 100, or 1000 - writing them as sums or differences of round numbers makes mental multiplication much faster.

Question. Use this method (writing numbers as sum/difference from round numbers) to find the following products.
(a) 95 x 8
Answer: Write 95 as 100 - 5:
95 x 8 = (100 - 5) x 8 = (100 x 8) - (5 x 8) = 800 - 40 = 760
In simple words: Use the round number 100, find 100 x 8 = 800, subtract the extra part 5 x 8 = 40, and you get 760.

Exam Tip: This method works best when one number is close to a round number like 10, 50, or 100.

Question. (b) 104 x 15
Answer: Write 104 as 100 + 4:
104 x 15 = (100 + 4) x 15 = (100 x 15) + (4 x 15) = 1500 + 60 = 1560
In simple words: Multiply 100 by 15 to get 1500, multiply the extra 4 by 15 to get 60, and add them together.

Exam Tip: When the number is slightly above a round number, add the parts; when it's slightly below, subtract them.

Question. (c) 49 x 50
Answer: Write 49 as 50 - 1:
49 x 50 = (50 - 1) x 50 = (50 x 50) - (1 x 50) = 2500 - 50 = 2450
In simple words: Multiply 50 by 50 to get 2500, subtract 1 x 50 = 50, giving you 2450.

Exam Tip: Multiplying by 50 is easy - it's half of 100, so you can use the round number 100 as a stepping stone if needed.

Question. Is this quicker than the multiplication procedure you use generally?
Answer: For many people, yes - this method is quicker, especially for mental multiplication. The reason is that it breaks the problem into simpler steps: multiplying by multiples of 10 or 100, which requires only shifting digits, plus or minus a smaller multiplication. This avoids the multi-step column multiplication many people learn in school.
In simple words: If you need to multiply in your head, using round numbers is faster than the long multiplication method taught in school.

Exam Tip: Speed in mental math comes from recognizing patterns - round numbers are the easiest to work with.

Question. Which other products might be quicker to find like the ones above?
Answer: This method is useful whenever one of the numbers is close to a multiple of 10, 100, 1000, etc. Examples include:
- 38 x 7 = (40 - 2) x 7
- 102 x 9 = (100 + 2) x 9
- 19 x 15 = (20 - 1) x 15
- 998 x 4 = (1000 - 2) x 4
Whenever you spot a number that is 1, 2, or a few units away from a round number, this method will simplify your work.
In simple words: If a number is close to 10, 100, or another round number, you can break it down and use the distributive property to make the math easier.

Exam Tip: Build a habit of scanning numbers for their distance from the nearest round number - this awareness is the first step to quick mental calculation.

Question 1. Fill in the blanks with numbers and boxes by signs, so that the expressions on both sides are equal (using the distributive property).
(a) 3 x (6 + 7) = 3 x 6 + 3 x 7 (Already filled)
(b) (8 + 3) x 4 = 8 x 4 + 3 x 4 (Already filled)
(c) 3 x (5 + 8) = 3 x 5 [+] 3 x [8]
(d) (9 + 2) x 4 = 9 x 4 [+] [2] x 4
(e) 3 x ([5] + 4) = 3 x [5] + [3 x 4]
(f) ([13] + 6) x 4 = 13 x 4 + [6 x 4]
(g) 3 x ([5] + [2]) = 3 x 5 + 3 x 2
(h) ([2] + [3]) x [4] = 2 x 4 + 3 x 4
(i) 5 x (9 - 2) = 5 x 9 - 5 x [2]
(j) (5 - 2) x 7 = 5 x 7 - 2 x [7]
(k) 5 x (8 - 3) = 5 x 8 [-] 5 x [3]
(l) (8 - 3) x 7 = 8 x 7 [-] [3] x 7
(m) 5 x (12 [-] [7]) = [5 x 12] [-] 5 x [7]
(n) (15 - [6]) x 7 = [15 x 7] [-] 6 x 7
(o) 5 x ([9] - [4]) = 5 x 9 - 5 x 4
(p) ([17] - [9]) x [7] = 17 x 7 - 9 x 7
Answer: The answers are shown in brackets above. The distributive property states that multiplying a number by a sum (or difference) is the same as multiplying by each part separately, then adding (or subtracting) the results.
In simple words: When you multiply by a bracket, you can multiply by each item inside, then add or subtract the results.

Exam Tip: Master the distributive property with both addition and subtraction - it's the foundation for expanding brackets and factoring.

Question 2. In the boxes below, fill '<','>' or '=' after analysing the expressions… Use reasoning… not by evaluating.
(a) (8 - 3) x 29 ___ (3 - 8) x 29
Answer: The answer is >. Reasoning: (8 - 3) = 5, which is positive. (3 - 8) = -5, which is negative. So (8 - 3) x 29 is a positive number multiplied by 29, while (3 - 8) x 29 is a negative number multiplied by 29. A positive number is always greater than a negative number, so the left side is greater than the right side.
In simple words: The left side multiplies a positive number by 29, while the right side multiplies a negative number by 29, so the left is bigger.

Exam Tip: Don't calculate the full answer - just figure out if each side will be positive or negative, and which is larger.

Question 2. (b) 15 + 9 x 18 ___ (15 + 9) x 18
Answer: The answer is <. Reasoning: LHS = 15 + (9 x 18). RHS = (15 + 9) x 18 = 15 x 18 + 9 x 18. Comparing them: 15 + (9 x 18) versus (15 x 18) + (9 x 18). Since 15 is much smaller than 15 x 18, the left side is smaller than the right side.
In simple words: On the left, you only add 15 to the result. On the right, you multiply 15 by 18, which is much bigger.

Exam Tip: Use the distributive property to rewrite the right side and then compare term by term - don't compute the actual numbers.

Question 2. (c) 23 x (17 - 9) ___ 23 x 17 + 23 x 9
Answer: The answer is <. Reasoning: LHS = 23 x (17 - 9) = 23 x 8. RHS = 23 x 17 + 23 x 9 = 23 x (17 + 9) = 23 x 26. Since 8 is much smaller than 26, the left side is smaller than the right side.
In simple words: On the left, you multiply by the difference (8). On the right, you multiply by the sum (26), which is bigger.

Exam Tip: Notice that the right side is a sum in the distributive formula, not a subtraction - rewrite it to see the true comparison.

Question 2. (d) (34 - 28) x 42 ___ 34 x 42 - 28 x 42
Answer: The answer is =. Reasoning: The right side is the expanded form of the left side using the distributive property. LHS = (34 - 28) x 42 = 6 x 42. RHS = (34 - 28) x 42 = 6 x 42. Both sides are identical and equal each other.
In simple words: The right side just shows what the left side looks like when you multiply out the difference - they mean the same thing.

Exam Tip: The distributive property works both ways - you can expand or factor - knowing both directions helps you recognize when expressions are equal.

Question 3. Here is one way to make 14: 2 x (1 + 6) = 14. Are there other ways…? Fill them out below: (Using format _ x (_ + _) = 14 etc.)
Answer: Many ways exist. Here are examples:
(a) _ x (_ + _) = 14. Examples: 7 x (1 + 1) = 14 or 2 x (3 + 4) = 14
(b) _ x (_ + _) = 14. Examples: 1 x (10 + 4) = 14 or 7 x (0 + 2) = 14
(c) _ x (_ + _ + _) = 14. Examples: 2 x (1 + 2 + 4) = 14 or 1 x (5 + 6 + 3) = 14
(d) _ x (_ + _ + _) = 14. Examples: 7 x (1 + 1 + 0) = 14 or 2 x (2 + 3 + 2) = 14
In simple words: You can make 14 by multiplying different numbers and grouping sums in brackets - any combination that multiplies to 14 works.

Exam Tip: Think about the factors of 14 (1, 2, 7, 14) and how the numbers inside the brackets can be arranged to create those factors.

Question 4. Find out the sum of the numbers given in each picture below in at least two different ways. Describe how you solved it through expressions.
(a) Picture 1 (5 squares of '4', 4 circles of '8')
Answer: Way 1 (Group by number):
(Number of 4s x 4) + (Number of 8s x 8) = (5 x 4) + (4 x 8) = 20 + 32 = 52.
Way 2 (Sum rows): (Row 1) + (Row 2) + (Row 3) = (4 + 8 + 4) + (8 + 4 + 8) + (4 + 8 + 4) = 16 + 20 + 16 = 52.
In simple words: Count all the 4s, count all the 8s, and add them together. Or add each row and sum the rows - both ways give 52.

Exam Tip: Always look for different ways to group items - choosing the right grouping can make the calculation simpler.

Question 4. (b) Picture 2 (8 circles of '5', 8 circles of '6')
Answer: Way 1 (Group by number):
(Number of 5s x 5) + (Number of 6s x 6) = (8 x 5) + (8 x 6) = 40 + 48 = 88.
Way 2 (Use distributive property): (8 x 5) + (8 x 6) = 8 x (5 + 6) = 8 x 11 = 88.
Way 3 (Sum rows): Each row has 5 + 6 + 6 + 5 = 22 (or 6 + 5 + 5 + 6 = 22). With 4 rows: 4 x 22 = 88. Expression: 4 x (5 + 6 + 6 + 5).
In simple words: You can count 8 fives and 8 sixes, or you can notice that both appear 8 times and multiply 8 by their sum, or you can add each row.

Exam Tip: The distributive property makes Way 2 shorter - look for repeated factors that can be factored out.

Question 1. Read the situations given below. Write appropriate expressions for each of them and find their values.
(a) The district market operates 7 days/week. Rahim supplies 9 kg mangoes/day, Shyam supplies 11 kg/day. Find amount supplied by them in a week.
Answer: Method 1: Expression = (Total daily supply) x Days = (9 + 11) x 7. Value = 20 x 7 = 140 kg.
Method 2: Expression = (Rahim's weekly) + (Shyam's weekly) = (9 x 7) + (11 x 7). Value = 63 + 77 = 140 kg.
Either expression is appropriate - both give 140 kg supplied in one week.
In simple words: Add what they supply each day (20 kg) and multiply by 7 days. Or multiply each person's daily supply by 7 and add the weekly amounts.

Exam Tip: Multiple correct approaches often exist for word problems - choose the one that feels simpler to you.

Question 1. (b) Binu earns Rs 20,000/month. Spends Rs 5,000 rent, Rs 5,000 food, Rs 2,000 other. What is the amount Binu will save by the end of a year?
Answer: Monthly Expenses = 5000 + 5000 + 2000 = 12000. Monthly Savings = Monthly Earnings - Monthly Expenses = 20000 - 12000 = 8000. Yearly Savings = Monthly Savings x 12. Expression: (20000 - (5000 + 5000 + 2000)) x 12 OR 12 x (20000 - 5000 - 5000 - 2000). Value = 12 x 8000 = Rs 96,000.
In simple words: Find what Binu saves each month (earnings minus expenses), then multiply by 12 months to get yearly savings.

Exam Tip: For word problems about money and time, always identify the time period first (per month, per week) and scale accordingly.

Question 1. (c) Snail climbs 3 cm up day, slips 2 cm night. Post is 10 cm high. In how many days will the snail get the treat?
Answer: Net climb per full day-night cycle = 3 cm - 2 cm = 1 cm. Tracking progress:
- End of Day 1: 3 cm. End of Night 1: 1 cm.
- End of Day 2: 4 cm. End of Night 2: 2 cm.
- End of Day 3: 5 cm. End of Night 3: 3 cm.
- End of Day 4: 6 cm. End of Night 4: 4 cm.
- End of Day 5: 7 cm. End of Night 5: 5 cm.
- End of Day 6: 8 cm. End of Night 6: 6 cm.
- End of Day 7: 9 cm. End of Night 7: 7 cm.
- During Day 8: Snail starts at 7 cm, climbs 3 cm, reaching 10 cm (the top) and gets the treat. It will get the treat on Day 8.
In simple words: Each full day and night, the snail makes 1 cm of progress. But once it climbs high enough during the day to reach the top, it gets the treat that same day.

Exam Tip: For climbing or rate problems, track both daytime and nighttime progress - the key is recognizing when the goal is reached during the day before slipping happens.

Question 2. Melvin reads a two-page story every day except on Tuesdays and Saturdays. How many stories would he complete reading in 8 weeks? Which of the expressions below describes this scenario?
Options: (a) 5 x 2 x 8 (b) (7 - 2) x 8 (c) 8 x 7 (d) 7 x 2 x 8 (e) 7 x 5 - 2 (f) (7 + 2) x 8 (g) 7 x 8 - 2 x 8 (h) (7 - 5) x 8
Answer: Reading days per week = 7 days - 2 non-reading days = 5 days. Pages per week = 5 days/week x 2 pages/day = 10 pages/week. Since a story is 2 pages, stories per week = 10 / 2 = 5 stories/week. Stories in 8 weeks = 5 stories/week x 8 weeks = 40 stories. Checking expressions: (b) (7 - 2) x 8 = 5 x 8 = 40 stories. This matches. Also, (g) 7 x 8 - 2 x 8 = (7 - 2) x 8 = 5 x 8 = 40, which is the same using the distributive property. Expressions describing the scenario (total stories = 40): (b) and (g).
In simple words: There are 5 reading days per week. Multiply 5 by 8 weeks to get 40 stories total.

Exam Tip: Word problems about schedules require you to identify non-working days first, then subtract to find working days.

Question 3. Find different ways of evaluating the following expressions.
(a) 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10
Answer: Way 1 (Left-to-right):
= -1 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10
= 2 - 4 + 5 - 6 + 7 - 8 + 9 - 10
= -2 + 5 - 6 + 7 - 8 + 9 - 10
= 3 - 6 + 7 - 8 + 9 - 10
= -3 + 7 - 8 + 9 - 10
= 4 - 8 + 9 - 10
= -4 + 9 - 10
= 5 - 10
= -5
Way 2 (Grouping pairs):
= (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + (9 - 10)
= (-1) + (-1) + (-1) + (-1) + (-1)
= -5
Way 3 (Positives and Negatives):
= (1 + 3 + 5 + 7 + 9) - (2 + 4 + 6 + 8 + 10)
= 25 - 30
= -5
In simple words: You can go left-to-right, group pairs of consecutive terms, or separate all positive numbers from negative ones and compute each sum.

Exam Tip: For long alternating sequences, grouping pairs is often the fastest method - it reveals a repeating pattern immediately.

Question 3. (b) 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1
Answer: Way 1 (Left-to-right):
= 0 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1
= 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1
= 0 + 1 - 1 + 1 - 1 + 1 - 1 = ... = 0
Way 2 (Grouping pairs):
= (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1)
= 0 + 0 + 0 + 0 + 0 = 0
In simple words: When you pair each 1 with a -1, each pair equals zero, so the whole thing equals zero.

Exam Tip: Grouping pairs is the faster method here - it shows the pattern clearly without tedious step-by-step subtraction.

Question 4. Compare the following pairs of expressions using '<', '>' or '=' or by reasoning.
(a) 49 - 7 + 8 ___ 49 - (7 + 8)
Answer: The answer is >. LHS = 42 + 8 = 50. RHS = 49 - 15 = 34. Reasoning: Subtracting 7 first, then adding 8 is different from subtracting the sum (7 + 8) at once. On the left, you subtract less total; on the right, you subtract more, so the left is larger.
In simple words: The left side subtracts 7 but adds back 8. The right side subtracts both 7 and 8 together, which is a larger subtraction.

Exam Tip: Brackets change which numbers combine - always think about what gets subtracted or added together.

Question 4. (b) 83 x 42 - 18 ___ 83 x 40 - 18
Answer: The answer is >. Reasoning: The only difference is 83 x 42 versus 83 x 40. Since 42 > 40, we have 83 x 42 > 83 x 40. Subtracting 18 from both does not change which is larger - if A > B, then A - 18 > B - 18. So the left side is greater.
In simple words: The left side multiplies by 42, while the right side multiplies by 40. Larger multiplication means a larger final answer.

Exam Tip: When comparing expressions, focus on the parts that differ - ignore identical parts like the "- 18".

Question 4. (c) 145 - 17 x 8 ___ 145 - 17 x 6
Answer: The answer is <. Reasoning: When subtracting, we compare -17 x 8 versus -17 x 6. Since 17 x 8 = 136 and 17 x 6 = 102, subtracting 136 is a larger subtraction than subtracting 102. When you subtract a larger value, the result becomes smaller. So the left side is smaller than the right side.
In simple words: On the left, you subtract more (17 x 8). On the right, you subtract less (17 x 6). Subtracting more leaves you with a smaller answer.

Exam Tip: For subtraction comparisons, the one with the larger subtracted value is smaller overall.

Question 4. (d) 23 x 48 - 35 ___ 23 x (48 - 35)
Answer: The answer is >. Reasoning: LHS = (23 x 48) - 35. RHS = 23 x 13. Since 23 x 48 is much larger than 23 x 13, subtracting 35 from the left side still leaves it far larger than the right side. The left is greater.
In simple words: The left side multiplies by 48 first, then subtracts only 35. The right side multiplies by only 13. So the left is much bigger.

Exam Tip: Brackets drastically change what gets multiplied - when comparing, identify what each side actually multiplies by.

Question 4. (e) (16 - 11) x 12 ___ -11 x 12 + 16 x 12
Answer: The answer is =. Reasoning: The right side can be rewritten using the distributive property as -11 x 12 + 16 x 12 = (16 - 11) x 12, which is identical to the left side. They are equal.
In simple words: The right side is just the left side expanded using the distributive property - they mean the same thing.

Exam Tip: If you see a pattern that looks like the distributive property, rewrite it to check if expressions are equal.

Question 4. (f) (76 - 53) x 88 ___ 88 x (53 - 76)
Answer: The answer is >. Reasoning: LHS = 23 x 88 (positive). RHS = 88 x (-23) (negative). A positive number is always greater than a negative number, so the left side is greater than the right side.
In simple words: The left side multiplies two positive numbers, giving a positive result. The right side multiplies by a negative number, giving a negative result. Positive is bigger.

Exam Tip: Check whether each side is positive or negative before doing detailed calculations - sign alone often determines the answer.

Question 4. (g) 25 x (42 + 16) ___ 25 x (43 + 15)
Answer: The answer is =. Reasoning: LHS = 25 x 58. RHS = 25 x 58. The sums inside the brackets are equal (42 + 16 = 58 and 43 + 15 = 58), so multiplying by 25 gives the same result on both sides.
In simple words: The numbers inside the brackets add to the same total on both sides, so the final answers are the same.

Exam Tip: For expressions with brackets, always check what the brackets actually contain - sometimes rearrangement hides identical totals.

Question 4. (h) 36 x (28 - 16) ___ 35 x (27 - 15)
Answer: The answer is >. Reasoning: LHS = 36 x 12. RHS = 35 x 12. Since 36 > 35, and both are multiplied by 12, the left side is greater than the right side.
In simple words: Both sides multiply by 12 (the bracket parts are equal), but the left multiplies 36 while the right multiplies 35, so the left is bigger.

Exam Tip: When brackets hold equal expressions, compare the multipliers - the larger multiplier gives the larger result.

Question 5. Identify which of the following expressions are equal to the given expression without computation. You may rewrite the expressions using terms or removing brackets.
(a) Given: 83 - 37 - 12 Options: (i) 84 - 38 - 12, (ii) 84 - (37 + 12), (iii) 83 - 38 - 13, (iv) -37 + 83 - 12
Answer: The terms of the given expression are (83), (-37), and (-12). Let's examine the terms of each option:
(i) Terms: (84), (-38), (-12). Not the same terms as the given expression.
(ii) 84 - (37 + 12) = 84 - 37 - 12. Terms: (84), (-37), (-12). Not the same - the first term is different.
(iii) Terms: (83), (-38), (-13). Not the same - the second and third terms are different.
(iv) Terms: (-37), (83), (-12). These are the same terms as the given expression, just rearranged. This is equal to the given expression.
Expression equal to the given one: (iv) -37 + 83 - 12.
In simple words: Two expressions are equal if they have the same terms (even in a different order). Check each option by breaking it into terms and comparing.

Exam Tip: Terms can be rearranged without changing the value (commutative property) - this is a quick way to spot equal expressions without full calculation.

Question 5. (b) Given: 93 + 37 x 44 + 76 Options: (i) 37 + 93 x 44 + 76, (ii) 93 + 37 x 76 + 44, (iii) (93 + 37) x (44 + 76), (iv) 37 x 44 + 93 + 76
Answer: The terms of the given expression are (93), (37 x 44), and (76). Let's examine the terms of each option:
(i) Terms: (37), (93 x 44), (76). Not the same - the multiplied term is different.
(ii) Terms: (93), (37 x 76), (44). Not the same - the multiplied term and second addition term are different.
(iii) This expression involves multiplying two sums together - the structure is completely different.
(iv) Terms: (37 x 44), (93), (76). These are the same terms as the given expression, just rearranged. This is equal to the given expression.
Expression equal to the given one: (iv) 37 x 44 + 93 + 76.
In simple words: The terms include a multiplication (37 x 44) and two additions (93 and 76). Only option (iv) has these same three terms in a different order.

Exam Tip: For expressions with multiplication and addition, identify the "term" as the whole product (37 x 44), not as separate factors - this helps you spot which expressions have the same terms.

Question 6. Choose a number and create ten different expressions having that value.
Answer: Let's choose the number 15. Here are ten different expressions that all equal 15:
1. 10 + 5
2. 20 - 5
3. 3 x 5
4. 30 / 2
5. 7 + 8
6. 1 + (2 x 7)
7. (5 x 5) - 10
8. 45 / (1 + 2)
9. 12 + 6 / 2
10. 2 x 8 - 1
In simple words: You can write any number in many ways - through addition, subtraction, multiplication, division, and combinations with brackets.

Exam Tip: Creating different expressions for the same number helps you see relationships between operations - addition and subtraction are opposites, multiplication and division are opposites.

What is taught in Class 7 Maths Ganita Prakash Chapter 2 Arithmetic Expressions?

Class 7 Maths Ganita Prakash Chapter 2 Arithmetic Expressions teaches students how to form, read and evaluate arithmetic expressions using basic operations like addition, subtraction, multiplication and division. It explains how brackets and the concept of terms are important to correctly understand and solve expressions. Students also learn different properties like commutative, associative and distributive properties, which help simplify complex expressions. Class 7 Maths Ganita Prakash NCERT Chapter 2 builds logical thinking by showing how expressions can be compared without full calculations and how small changes in terms affect the final value. Real-life examples make understanding easier and more relatable for students.