Numerical Expressions — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
(15 − 5) ÷ 2 means divide 15 by 2, then subtract 5
Corrected: (15 − 5) ÷ 2 means subtract 5 from 15, then divide by 2
The parentheses around (15 − 5) mean you subtract first to get 10, then divide by 2. The original wrongly did the division before the subtraction.
2. Fix the sentence:
Multiply 4 by 8, then add 3 is written as 4 × 8 × 3
Corrected: Multiply 4 by 8, then add 3 is written as (4 × 8) + 3
The second step says to add 3, not multiply by 3. Writing (4 × 8) + 3 correctly uses addition as the second operation.
3. Fix the sentence:
Add 7 and 13, then divide by 10 is written as 7 + (13 ÷ 10)
Corrected: Add 7 and 13, then divide by 10 is written as (7 + 13) ÷ 10
The addition of 7 and 13 must happen first, so both numbers go inside the parentheses. Then you divide the entire sum by 10.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Add 16 and 4, then multiply by 5 is written as (16 + 4) × 5.
Since the addition of 16 and 4 needs to happen before multiplying, parentheses group them together: (16 + 4) × 5.
2. Subtract 9 from 21, then divide by 6 is written as (21 − 9) ÷ 6.
Parentheses around (21 − 9) force the subtraction first, giving 12, which is then divided by 6.
3. Divide 40 by 8, then subtract 1 is written as (40 ÷ 8) − 1.
The division of 40 by 8 happens first inside the parentheses, giving 5, and then you subtract 1 from that quotient.
4. Multiply 3 by 9, then add 6 is written as (3 × 9) + 6.
Parentheses around (3 × 9) ensure the multiplication happens first, producing 27, and then 6 is added to that product.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Write a numerical expression for: Divide 24 by 6, then add 9. Explain what your expression means.
Sample answer: (24 ÷ 6) + 9. This means you first find the quotient of 24 and 6, which is 4, then add 9 to that quotient.
A good answer includes: (24 ÷ 6) + 9. This means you first find the quotient of 24 and 6, which is 4, then add 9 to that quotient.
2. Write a numerical expression for: Subtract 3 from 15, then multiply by 4. Explain what it represents.
Sample answer: (15 − 3) × 4. This means you first find the difference of 15 and 3, which is 12, then multiply that difference by 4.
A good answer includes: (15 − 3) × 4. This means you first find the difference of 15 and 3, which is 12, then multiply that difference by 4.