Numerical Expressions — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
(8 + 7) × 4 means add 8 and 4, then multiply by 7
Corrected: (8 + 7) × 4 means add 8 and 7, then multiply by 4
The corrected sentence is: "(8 + 7) × 4 means add 8 and 7, then multiply by 4". The original sentence "(8 + 7) × 4 means add 8 and 4, then multiply by 7" contained an error that needed to be fixed.
2. Fix the sentence:
Subtract 3 from 10, then multiply by 5 is written as 10 − 3 + 5
Corrected: Subtract 3 from 10, then multiply by 5 is written as (10 − 3) × 5
The corrected sentence is: "Subtract 3 from 10, then multiply by 5 is written as (10 − 3) × 5". The original sentence "Subtract 3 from 10, then multiply by 5 is written as 10 − 3 + 5" contained an error that needed to be fixed.
3. Fix the sentence:
Divide 20 by 4, then add 6 is written as 20 ÷ (4 + 6)
Corrected: Divide 20 by 4, then add 6 is written as (20 ÷ 4) + 6
The corrected sentence is: "Divide 20 by 4, then add 6 is written as (20 ÷ 4) + 6". The original sentence "Divide 20 by 4, then add 6 is written as 20 ÷ (4 + 6)" contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Add 9 and 3, then multiply by 2 is written as (9 + 3) × 2.
The phrase 'then multiply by 2' means the addition must happen first. Parentheses group the addition: (9 + 3) × 2.
2. Subtract 5 from 12, then divide by 7 is written as (12 − 5) ÷ 7.
Subtract first, then divide. Parentheses group the subtraction: (12 − 5) ÷ 7.
3. Multiply 6 by 4, then add 10 is written as (6 × 4) + 10.
Multiply first, then add. Since multiplication is being done first anyway, the expression could also be written as 6 × 4 + 10, but parentheses clarify the order: (6 × 4) + 10.
4. Divide 18 by 3, then subtract 2 is written as (18 ÷ 3) − 2.
Divide first, then subtract. Parentheses group the division: (18 ÷ 3) − 2.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Write a numerical expression for: Add 15 and 5, then divide by 4. Explain what your expression means.
Sample answer: (15 + 5) ÷ 4. This means you first find the sum of 15 and 5, which is 20, then divide that sum by 4.
Parentheses ensure the addition is performed before the division: (15 + 5) ÷ 4 = 20 ÷ 4 = 5.
2. Write a numerical expression for: Multiply 7 by 3, then subtract 8. Explain what it represents.
Sample answer: (7 × 3) − 8. This means you first find the product of 7 and 3, which is 21, then subtract 8 from that product.
Multiply before subtracting: (7 × 3) − 8 = 21 − 8 = 13.