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Class 7 Maths: Arithmetic Expressions, 8 practice questions with answers

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These are 8 practice questions on Chapter 2, Arithmetic Expressions, of the new NCERT Class 7 Maths textbook, Ganita Prakash, Part 1. Each has a worked answer and the textbook page it comes from. They cover the terms of a bill with a division in it, a bracket of three terms after a minus sign, nested brackets, totalling a passbook by grouping, the distributive property turned round, choosing the expression for an area, changing both factors of a known product, and comparing products without working them out. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script. Each question has its own setting, not one of the chapter's worked examples or exercises with new numbers. No practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 7, Part 1, Chapter 2, printed pages 24 to 45):

Terms and brackets

Question 1. Ravi's stationery bill is written as one expression: 3 × 45 + 120 ÷ 4 − 15. (He bought 3 pens at ₹45, paid his quarter share of a ₹120 pack of chart paper bought by 4 friends, and got ₹15 off.) (a) Write the expression as a sum of terms. (b) Find its value.

Answer: (a) 3 × 45, 120 ÷ 4 and −15; (b) ₹150. (a) Turning the subtraction into adding the opposite, the expression is 3 × 45 + 120 ÷ 4 + (−15), so its terms are 3 × 45, 120 ÷ 4 and −15. The division belongs to its own term, just as a multiplication does. (b) Each term is worked out first: 3 × 45 = 135, 120 ÷ 4 = 30, and −15. Then the terms are added: 135 + 30 + (−15) = 150. Doing the steps from left to right instead, (3 × 45 + 120) ÷ 4 − 15, would give 63.75 − 15 = 48.75, which is not his bill. (Terms of an expression, pages 28 and 31.)

Question 2. A water tank shows 60 cm on its gauge. In one afternoon, one tap drains 12 cm, a second tap drains 7 cm, and a short shower of rain adds 4 cm. (a) Write the net fall as one bracket, and the final level as 60 minus that bracket. (b) Remove the bracket and check that you get the same level.

Answer: (a) net fall (12 + 7 − 4) cm, level 60 − (12 + 7 − 4) = 45 cm; (b) 60 − 12 − 7 + 4 = 45 cm. (a) The level falls by 12 and by 7 and rises by 4, so the net fall is 12 + 7 − 4 = 15 cm, and the level is 60 − (12 + 7 − 4) = 60 − 15 = 45 cm. (b) When a bracket after a minus sign is removed, the sign of every term inside changes: +12 becomes −12, +7 becomes −7, and −4 becomes +4. So 60 − (12 + 7 − 4) = 60 − 12 − 7 + 4 = 45 cm, the same. The +4 makes sense: the rain made the fall smaller, so it makes the final level higher. (Removing a bracket after a minus sign, pages 35 and 36.)

Question 3. Simplify 100 − (30 − (12 + 5)) in two ways: (a) working out the innermost bracket first; (b) removing the brackets, starting with the inner one, using the sign rule. Check that both give the same value.

Answer: both give 87. (a) Innermost first: 12 + 5 = 17, then 30 − 17 = 13, then 100 − 13 = 87. (b) The inner bracket follows a minus sign inside the outer bracket, so its signs change: 30 − (12 + 5) = 30 − 12 − 5. The expression is now 100 − (30 − 12 − 5). That bracket also follows a minus sign, so every sign inside changes again: 100 − 30 + 12 + 5 = 87. The 12 and the 5 are subtracted twice over, so they end up being added. (Brackets and the sign rule, pages 35 and 36.)

Adding, products and stories

Question 4. A shop's bank passbook shows these entries for a week: a credit of ₹2,500, a debit of ₹780, a credit of ₹1,200, a debit of ₹220 and a debit of ₹1,000. (a) Write the week's net change as a sum of positive and negative terms. (b) Group the terms in a smart way to find it, and name the properties that let you regroup.

Answer: (a) 2,500 + (−780) + 1,200 + (−220) + (−1,000); (b) +₹1,700. (a) Credits are positive and debits negative, so the net change is 2,500 + (−780) + 1,200 + (−220) + (−1,000). (b) Group the credits: 2,500 + 1,200 = 3,700. Group the debits: (−780) + (−220) = −1,000, and with the other −1,000 they make −2,000. Then 3,700 + (−2,000) = 1,700, so the balance went up by ₹1,700. Swapping terms uses the commutative property and regrouping them uses the associative property of addition; neither changes the sum. (Swapping and grouping terms, pages 29 to 31.)

Question 5. A farmer plants 37 rows of saplings on Monday and 63 rows on Tuesday, with 46 saplings in every row. (a) Write the total as the sum of two products. (b) Use the distributive property to find it quickly.

Answer: (a) 37 × 46 + 63 × 46; (b) 4,600. (a) Monday's saplings are 37 × 46 and Tuesday's are 63 × 46, so the total is 37 × 46 + 63 × 46. (b) Both products share the factor 46, so by the distributive property the sum of the multiples is the multiple of the sum: 37 × 46 + 63 × 46 = (37 + 63) × 46 = 100 × 46 = 4,600. In the story, this is counting all 100 rows at once. (The distributive property, pages 39 to 41.)

Question 6. A rectangular garden is 8 m long and 5 m wide. A rectangular pond 3 m by 2 m is dug inside it. Which expression gives the area of grass left: (i) 8 × (5 − 2); (ii) 8 × 5 − 3 × 2; (iii) (8 − 3) × (5 − 2)? Find the area, and say what each wrong expression measures instead.

Answer: (ii), 34 square metres. The grass is the whole garden minus the pond: 8 × 5 − 3 × 2 = 40 − 6 = 34 m², with two terms, 8 × 5 and −3 × 2. (i) 8 × (5 − 2) = 24 is the area of a strip 8 m long and 3 m wide, as if a 2 m band were cut off right across the garden. (iii) (8 − 3) × (5 − 2) = 15 is the area of a 5 m by 3 m rectangle, which is neither the grass nor the pond. The brackets change which numbers are multiplied together. (Terms and brackets, pages 28, 31 and 39.)

Question 7. It is known that 25 × 36 = 900. Without multiplying from scratch, find 26 × 35. Explain each step.

Answer: 910. Change one factor at a time. First 26 × 36: one more 36 than 25 × 36, so 900 + 36 = 936. Then 26 × 35: one fewer 26 than 26 × 36, so 936 − 26 = 910. Check another way: 25 × 35 = 900 − 25 = 875, and 26 × 35 = 875 + 35 = 910. Both factors changed, one up by 1 and one down by 1, yet the product went up, by 10. (Changing a number in a product, the distributive property, pages 40 and 41.)

Question 8. Without working out the full products, decide which is bigger and by how much: (a) 48 × 52 or 50 × 50; (b) 39 × 41 or 40 × 40.

Answer: (a) 50 × 50, by 4; (b) 40 × 40, by 1. (a) Write both against 50 × 52. 48 × 52 is 2 fewer 52s: 50 × 52 − 104. 50 × 50 is 2 fewer 50s: 50 × 52 − 100. The first takes away 4 more, so 50 × 50 is bigger by 4 (2,500 and 2,496). (b) In the same way, 39 × 41 = 40 × 41 − 41 and 40 × 40 = 40 × 41 − 40, so 40 × 40 is bigger by 1 (1,600 and 1,599). (Comparing products with the distributive property, pages 40 and 41.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 23 for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Arithmetic Expressions, Class 7 worksheet. Printable, in English, Hindi and Marathi, with an answer key.