Arithmetic Expressions — Hard

Q1. Consider the following statements about removing brackets: I. In 14 − (12 + 10), removing the brackets gives 14 − 12 − 10. II. In 14 + (12 − 10), removing the brackets gives 14 + 12 + 10. III. In 14 − (12 − 10), removing the brackets gives 14 − 12 + 10. Which of the statements are correct?

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

Q2. Which of the following expressions is equal in value to 5 × (9 − 2)?

• A. 5 × 9 − 2
• B. 5 × 9 − 5 × 2
• C. 5 + 9 − 5 × 2
• D. (5 − 2) × 9

Q3. Read the two statements: Assertion (A): The value of the expression 30 + 5 × 4 is 50. Reason (R): In any expression, addition must be performed before multiplication. Choose the correct option.

• A. Both A and R are true, and R is the correct explanation of A.
• B. Both A and R are true, but R is NOT the correct explanation of A.
• C. A is true, R is false.
• D. A is false, R is true.

Q4. By reasoning about terms and brackets, compare 23 × 48 − 35 with 23 × (48 − 35).

• A. 23 × 48 − 35 > 23 × (48 − 35)
• B. 23 × 48 − 35 < 23 × (48 − 35)
• C. 23 × 48 − 35 = 23 × (48 − 35)
• D. Cannot be decided without computing

Q5. Without computing, find the number that fills both blanks so that 423 + ___ = 419 + ___ is true, given the second blank should be 4 more than the first.

• A. First blank 4, second blank 8
• B. First blank 0, second blank 4
• C. First blank 5, second blank 9
• D. Any pair where the second is 4 more than the first

Q6. Consider the statements about distributivity over subtraction: I. 23 × (17 − 9) = 23 × 17 − 23 × 9. II. 23 × (17 − 9) = 23 × 17 − 9. III. 23 × (17 − 9) = (23 − 9) × 17. Which are correct?

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

Q7. Given that 53 × 18 = 954, find 63 × 18 using the 'tinker the terms' idea from Example 17.

• A. 954 + 18
• B. 954 + 180
• C. 954 + 53
• D. 954 × 10

Q8. A snail climbs 3 cm up a post during the day and slips 2 cm down at night. The post is 10 cm high and a treat is on top. In how many days does the snail reach the treat?

• A. 5 days
• B. 7 days
• C. 8 days
• D. 10 days

Q9. Whenever Jasoda has to subtract 9 from a number, she instead subtracts 10 and adds 1. For example 36 − 9 = 26 + 1. Why does this always give the correct answer?

• A. Because 10 − 1 = 9, so subtracting 10 and adding 1 is the same as subtracting 9.
• B. Because subtraction is commutative.
• C. Because 9 and 10 are consecutive numbers, so we can use either.
• D. It does not always work — it only works for two-digit numbers.

Q10. What is the value of the expression 14 − (12 + 10)?

• A. 12
• B. −8
• C. 8
• D. −14

Q11. By reasoning about terms, compare 145 − 17 × 8 and 145 − 17 × 6 without evaluating.

• A. 145 − 17 × 8 > 145 − 17 × 6
• B. 145 − 17 × 8 < 145 − 17 × 6
• C. 145 − 17 × 8 = 145 − 17 × 6
• D. Cannot be decided without computing

Q12. The Begur market runs all seven days a week. Rahim supplies 9 kg of mangoes each day and Shyam supplies 11 kg each day. Which expression gives the total mangoes (in kg) supplied to the market in a week?

• A. 9 + 11 + 7
• B. 9 × 11 × 7
• C. (9 + 11) × 7
• D. 9 × 7 + 11

Q13. Queen Alia gave 100 gold coins each to Princess Elsa and Princess Anna last year. Elsa doubled her coins through business. Anna spent half her coins on jewellery. Which expression gives the total coins the two princesses now have together?

• A. 100 + 100
• B. 2 × 100 + 100 ÷ 2
• C. 100 × 2 × (1/2)
• D. (2 + 1/2) × 100

Q14. For the expression (−7) + 10 + (−11), which of the following statements are true? I. Grouping the first two terms gives the same value as grouping the last two terms. II. The value of the expression is −8 no matter in which order the terms are added. III. Changing addition order changes the value because two terms are negative.

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

Q15. Using the method (100 − k) × n, the value of 95 × 8 is

• A. 760
• B. 780
• C. 750
• D. 800