Numerical Expressions — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Which expression represents: Divide the sum of 16 and 8 by the difference of 9 and 3?
A) (16 + 8) ÷ (9 − 3)
B) 16 + 8 ÷ 9 − 3
C) (16 ÷ 8) + (9 − 3)
D) (16 + 8) × (9 − 3)
"Sum of 16 and 8" translates to (16 + 8) and "difference of 9 and 3" translates to (9 − 3). Dividing the first by the second gives (16 + 8) ÷ (9 − 3).
2. Without calculating, which statement about (7 + 5) × 8 is true?
A) It equals 7 + 40
B) It is 8 times as large as (7 + 5)
C) It is 8 more than (7 + 5)
D) It equals 7 × 8 + 5
Multiplying any expression by 8 makes the result 8 times as large as that expression. Since (7 + 5) is being multiplied by 8, the product is 8 times (7 + 5).
3. What is the value of (18 ÷ 3) × (5 + 4)?
A) 27
B) 54
C) 45
D) 36
Solve each set of parentheses: 18 ÷ 3 = 6 and 5 + 4 = 9. Then multiply: 6 × 9 = 54.
4. Which expression has the smallest value? A = (20 − 8) × 3, B = (20 − 8) × 5, C = (20 − 8) × 2, D = (20 − 8) × 4
A) A = (20 − 8) × 3
B) B = (20 − 8) × 5
C) C = (20 − 8) × 2
D) D = (20 − 8) × 4
All four expressions have the same value inside the parentheses (20 − 8 = 12), so the smallest multiplier produces the smallest result. Multiplying 12 by 2 gives 24, the least of all four.
Part B: Fill in the Blank
Write the correct answer on each line.
1. Evaluate: (5 + 9) × (15 − 8) = 98
Solve each set of parentheses: 5 + 9 = 14 and 15 − 8 = 7. Then multiply: 14 × 7 = 98.
2. Evaluate: (36 ÷ 4) + (7 × 2) = 23
Solve each set of parentheses: 36 ÷ 4 = 9 and 7 × 2 = 14. Then add: 9 + 14 = 23.
3. Evaluate: (8 × 5) − (27 ÷ 3) = 31
Solve each set of parentheses: 8 × 5 = 40 and 27 ÷ 3 = 9. Then subtract: 40 − 9 = 31.
4. Write an expression: Find the quotient of the sum of 20 and 4 and the difference of 10 and 4. Answer: (20 + 4) ÷ (10 − 4)
"Sum of 20 and 4" becomes (20 + 4) and "difference of 10 and 4" becomes (10 − 4). "Quotient" means to divide the first group by the second.
5. Evaluate: (20 + 4) ÷ (10 − 4) = 4
Solve each set of parentheses: 20 + 4 = 24 and 10 − 4 = 6. Then divide: 24 ÷ 6 = 4.