Numerical Expressions — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
5 × (20 + 12) is 5 more than 20 + 12
Corrected: 5 × (20 + 12) is 5 times as large as 20 + 12
The corrected sentence is: "5 × (20 + 12) is 5 times as large as 20 + 12". The original sentence "5 × (20 + 12) is 5 more than 20 + 12" contained an error that needed to be fixed.
2. Fix the sentence:
(30 − 8) ÷ 2 is half the value of 30 + 8
Corrected: (30 − 8) ÷ 2 is half the value of 30 − 8
The corrected sentence is: "(30 − 8) ÷ 2 is half the value of 30 − 8". The original sentence "(30 − 8) ÷ 2 is half the value of 30 + 8" contained an error that needed to be fixed.
3. Fix the sentence:
3 × (14 + 6) has the same value as 3 × 14 + 6
Corrected: 3 × (14 + 6) has the same value as 3 × 14 + 3 × 6
The corrected sentence is: "3 × (14 + 6) has the same value as 3 × 14 + 3 × 6". The original sentence "3 × (14 + 6) has the same value as 3 × 14 + 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. Without calculating, 4 × (8 + 5) is 4 times as large as (8 + 5).
Multiplying an expression by 4 makes it 4 times as large. You don't need to calculate the value of (8 + 5) to know the relationship.
2. Without calculating, (36 − 9) ÷ 3 is one third of (36 − 9).
Dividing an expression by 3 gives one-third of its value. (36 − 9) ÷ 3 is one third of (36 − 9).
3. Without calculating, 7 × (10 + 2) is 7 times as large as 10 + 2.
Multiplying (10 + 2) by 7 produces a result that is 7 times as large as the sum alone.
4. Without calculating, (45 + 15) ÷ 6 is one sixth of (45 + 15).
Dividing by 6 produces one-sixth of the original expression's value.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Without calculating either expression, explain how 8 × (14 + 26) compares to (14 + 26).
Sample answer: 8 × (14 + 26) is 8 times as large as (14 + 26) because you are multiplying the sum of 14 and 26 by 8.
Multiplying an expression by 8 makes the result 8 times larger than the original expression, regardless of its actual value.
2. Without calculating, explain the relationship between (50 − 20) and (50 − 20) ÷ 5.
Sample answer: (50 − 20) ÷ 5 is one fifth of (50 − 20) because you are dividing the difference of 50 and 20 by 5.
Dividing an expression by 5 gives one-fifth of its value. The relationship holds regardless of the actual computed value.