Numerical Expressions — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The expression 3 × (12 − 4) means subtract 4 from 3, then multiply by 12
Corrected: The expression 3 × (12 − 4) means subtract 4 from 12, then multiply by 3
Parentheses tell you to do (12 − 4) first, subtracting 4 from 12, not from 3. Then you multiply that result by 3.
2. Fix the sentence:
Add 6 and 14, then divide by 5 is written as 6 + 14 ÷ 5
Corrected: Add 6 and 14, then divide by 5 is written as (6 + 14) ÷ 5
Without parentheses, order of operations would divide 14 by 5 first. Parentheses around (6 + 14) force the addition to happen before dividing by 5.
3. Fix the sentence:
Multiply 9 by 2, then add 7 is written as 9 × (2 + 7)
Corrected: Multiply 9 by 2, then add 7 is written as (9 × 2) + 7
The phrase says multiply first, then add 7 to the product. Putting 2 + 7 in parentheses would add before multiplying, which changes the meaning entirely.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Subtract 8 from 20, then multiply by 3 is written as (20 − 8) × 3.
The subtraction must happen first, so parentheses go around (20 − 8). Then you multiply that difference by 3.
2. Add 11 and 9, then divide by 4 is written as (11 + 9) ÷ 4.
You need to add 11 and 9 before dividing, so parentheses around (11 + 9) ensure the sum is found first, then divided by 4.
3. Divide 30 by 6, then add 8 is written as (30 ÷ 6) + 8.
Parentheses around (30 ÷ 6) show that division comes first, giving 5, and then 8 is added to that quotient.
4. Multiply 5 by 7, then subtract 12 is written as (5 × 7) − 12.
Parentheses around (5 × 7) make the multiplication happen first, producing 35, and then 12 is subtracted from that product.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Write a numerical expression for: Subtract 6 from 18, then divide by 3. Explain what your expression means.
Sample answer: (18 − 6) ÷ 3. This means you first find the difference of 18 and 6, which is 12, then divide that difference by 3.
A good answer includes: (18 − 6) ÷ 3. This means you first find the difference of 18 and 6, which is 12, then divide that difference by 3.
2. Write a numerical expression for: Add 8 and 12, then multiply by 2. Explain what it represents.
Sample answer: (8 + 12) × 2. This means you first find the sum of 8 and 12, which is 20, then multiply that sum by 2.
A good answer includes: (8 + 12) × 2. This means you first find the sum of 8 and 12, which is 20, then multiply that sum by 2.