Arithmetic Expressions — Mastery

Q1. The chapter shows that the number 12 can be written as 10 + 2, 15 − 3, 3 × 4 and 24 ÷ 2. Which of these expressions has the value 12?

• A. 10 + 2 only
• B. 15 − 3 and 3 × 4 only
• C. All four expressions
• D. 24 ÷ 2 only

Q2. Arrange the expressions 67 − 19, 67 − 20, 35 + 25, 5 × 11 and 120 ÷ 3 in ascending order of their values.

• A. 67 − 20, 67 − 19, 35 + 25, 120 ÷ 3, 5 × 11
• B. 120 ÷ 3, 67 − 20, 67 − 19, 5 × 11, 35 + 25
• C. 5 × 11, 35 + 25, 67 − 19, 67 − 20, 120 ÷ 3
• D. 67 − 20, 67 − 19, 5 × 11, 35 + 25, 120 ÷ 3

Q3. Why does writing the expression 100 − 15 + 56 (without brackets) give the absurd answer ₹141 for Irfan's change instead of the correct ₹29?

• A. Because 56 is a large number
• B. Because the addition is done before subtraction in any expression
• C. Because the terms are 100, −15 and 56 — so 56 is added rather than treated as part of the total cost
• D. Because the order of operations changes between addition and subtraction

Q4. Why does the chapter convert subtraction into 'adding the inverse' when identifying terms of an expression?

• A. Because subtraction is not allowed in mathematics
• B. Because it lets us separate terms using only the '+' sign — keeping a single, consistent definition of a term
• C. Because the inverse of a number is always positive
• D. Because the value of any expression changes when we add instead of subtract

Q5. Why is 6 × 5 considered a single term in an expression like 6 × 5 + 3?

• A. Because it has only two numbers
• B. Because it does not contain a '+' sign inside it
• C. Because multiplication is always done last
• D. Because all products are single terms regardless of context

Q6. Manasa's mother says, 'Wear your hat and shoes!' She can wear them in either order. Her mother then says, 'Wear your socks and shoes!' — now order matters. What is the best mathematical analogy from this chapter?

• A. Hat-and-shoes models the distributive property; socks-and-shoes models brackets.
• B. Hat-and-shoes models addition (commutative); socks-and-shoes shows that not all operations are commutative.
• C. Both situations show that subtraction is commutative.
• D. Both situations show that division and subtraction are the same.

Q7. Example 10 of the chapter writes 432 = 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1. What does this expression mean in terms of notes and coins?

• A. 4 notes of ₹100, 1 note of ₹20, 1 note of ₹10, and 2 coins of ₹1
• B. 4 notes of ₹10, 1 note of ₹20, 1 note of ₹100, and 2 coins of ₹1
• C. 432 ₹1 coins only
• D. 8 notes of ₹50, 1 note of ₹10, 4 coins of ₹5, and 2 coins of ₹1

Q8. Binu earns ₹20,000 per month. Each month she spends ₹5,000 on rent, ₹5,000 on food and ₹2,000 on other expenses. How much will she save by the end of one year?

• A. ₹96,000
• B. ₹1,20,000
• C. ₹84,000
• D. ₹2,40,000

Q9. Which two expressions have the SAME value as 100 − (15 + 56)? I. 100 − 15 − 56 II. 100 − 15 + 56 III. (100 − 15) − 56

• A. I and II only
• B. II and III only
• C. I and III only
• D. All three

Q10. Given 53 + (−16) = 37, the value of 53 + (−15) is

• A. 36
• B. 37
• C. 38
• D. 52

Q11. What value fills the blank to make the statement correct: 3 × (5 + 8) = 3 × 5 + ___?

• A. 3
• B. 8
• C. 24
• D. 39

Q12. Using the (100 + k) × n method, the value of 104 × 15 is

• A. 1,500
• B. 1,560
• C. 1,460
• D. 1,540

Q13. By reasoning about distributivity, compare (16 − 11) × 12 and −11 × 12 + 16 × 12.

• A. (16 − 11) × 12 > −11 × 12 + 16 × 12
• B. (16 − 11) × 12 < −11 × 12 + 16 × 12
• C. (16 − 11) × 12 = −11 × 12 + 16 × 12
• D. Cannot be decided without computing

Q14. Melvin reads a two-page story every day except Tuesdays and Saturdays. How many such stories does he complete in 8 weeks?

• A. 16
• B. 32
• C. 40
• D. 56

Q15. A metro train ticket between two stations is ₹40 for an adult and ₹20 for a child. Which expression gives the total cost for four adults and three children?

• A. (4 + 3) × (40 + 20)
• B. 4 × 40 + 3 × 20
• C. 4 × 20 + 3 × 40
• D. (40 + 20) × 7

Q16. Mallika spends ₹25 every day for lunch at school from Monday to Friday. As in Example 1, which arithmetic expression gives the total amount she spends in a week?

• A. 5 × 25
• B. 25 + 5
• C. 25 ÷ 5
• D. 25 − 5

Q17. Without computing, compare 364 + 587 and 363 + 589.

• A. 364 + 587 > 363 + 589
• B. 364 + 587 = 363 + 589
• C. Cannot be decided without computing
• D. 364 + 587 < 363 + 589

Q18. What is the value of the expression 200 − (40 + 3)?

• A. 157
• B. 163
• C. 243
• D. 237

Q19. Writing 23 − 2 × 4 + 16 as a sum of terms, the terms are

• A. 23, 2, 4 and 16
• B. 23, −2 × 4 and −16
• C. 23 − 2 and 4 + 16
• D. 23, −2 × 4 and 16

Q20. The chapter shows that (−7) + 10 + (−11) gives the same value whether we add the first two terms first or the last two first. What value does the expression equal?

• A. −8
• B. −28
• C. 8
• D. 28

Q21. Manasa's mother says, 'Wear your socks and shoes!' A child argues that any order works because addition is commutative. Which response is the best mathematical judgement, based on the chapter?

• A. The child is right — every everyday action is commutative.
• B. The child is right — order never matters in mathematics.
• C. The child is wrong — addition itself is not commutative.
• D. The child is wrong — socks-and-shoes must be done in a fixed order; commutativity of addition does not apply to all actions.

Q22. A window has a top border of 3 cm, a grill of 2 cm and a gap of 5 cm below the grill, as shown in Question 3(c). Which expression gives the total height of the window?

• A. 3 + 2 + 5
• B. 3 × 2 × 5
• C. (3 + 5) − 2
• D. 3 + 2 − 5

Q23. Removing the brackets in 14 + (12 + 10) gives which equivalent expression?

• A. 14 − 12 − 10
• B. 14 − 12 + 10
• C. 14 + 12 − 10
• D. 14 + 12 + 10

Q24. Using only reasoning about how terms change, find the number that fills the blank: 207 − 68 = 210 − ____.

• A. 71
• B. 65
• C. 68
• D. 63

Q25. The chapter shows 98 + 98 + ... (10 times) added to 98 + 98 + 98 (3 times). What equality does this picture lead to?

• A. 10 × 98 + 3 × 98 = 30 × 98
• B. 10 × 98 + 3 × 98 = 98 + 3
• C. 10 × 98 + 3 × 98 = 13 × 10
• D. 10 × 98 + 3 × 98 = (10 + 3) × 98

Q26. Using the (n − k) × m method from Example 18, the value of 49 × 50 is

• A. 2,450
• B. 2,500
• C. 2,550
• D. 2,400

Q27. Hira has 28 coins in one bag and 35 coins in another. She gifts 10 coins from the second bag to a friend. How many coins are left with Hira in total?

• A. 73
• B. 63
• C. 43
• D. 53

Q28. By reasoning about terms and brackets, compare (8 − 3) × 29 and (3 − 8) × 29.

• A. (8 − 3) × 29 > (3 − 8) × 29
• B. (8 − 3) × 29 = (3 − 8) × 29
• C. (8 − 3) × 29 < (3 − 8) × 29
• D. Cannot be decided without computing

Q29. By reasoning about terms (no computing), compare 25 × (42 + 16) and 25 × (43 + 15).

• A. 25 × (42 + 16) > 25 × (43 + 15)
• B. 25 × (42 + 16) < 25 × (43 + 15)
• C. Cannot be decided
• D. 25 × (42 + 16) = 25 × (43 + 15)

Q30. A Class 7 student says, 'To list the terms of 83 − 14, I should just remove the minus sign and call the terms 83 and 14.' Which response best evaluates this strategy?

• A. The strategy is wrong — the second term must be the inverse −14, not 14, so that the terms add to give the original expression.
• B. The strategy is correct — terms are always positive.
• C. The strategy is correct because 14 is smaller than 83.
• D. The strategy is wrong because we should write 14 − 83 instead.