Rewriting Sums with the Distributive Property: Sample FAST Questions
Students rewrite the sum of two composite whole numbers that share a common factor as that common factor multiplied by a sum. For example, 24 + 36 can be rewritten as 12(2 + 3). This connects factoring with the distributive property and builds groundwork for algebra.
How the FAST tests this benchmark
On the FAST, students see multiple choice items asking which expression is equivalent to a given sum, and equation editor items where they write the factored form themselves.
Skills students need
Rewrite a sum of two numbers using a common factor and the distributive property
Try 4 real MA.6.NSO.3.2 questions
These come straight from Algebro's question bank. Pick an answer to check it instantly.
Question 1EasyMultiple Choice
Which expression correctly rewrites 12+18 using the greatest common factor?
Correct answer: A. 6(2+3)
This explanation shows one way to solve the problem.
Find GCF(12, 18): Factors of 12: 1,2,3,4,6,12 Factors of 18: 1,2,3,6,9,18 → GCF =6
Factor out the GCF: 12+18=6(2+3)
Final Answer
6(2 + 3)
Question 2MediumMultiple Choice
Which sum is equivalent to 2(11+14)?
Correct answer: B. 22+28
This explanation shows one way to solve the problem.
Apply the distributive property: Distribute the 2 to each term inside the parentheses: 2(11+14)=2×11+2×14
Multiply each term: 2×11=22 and 2×14=28. So 2(11+14)=22+28
Final Answer
22 + 28
Question 3MediumMultiple Choice
Which sum is equivalent to 3(8+11)?
Correct answer: B. 24+33
This explanation shows one way to solve the problem.
Apply the distributive property: Distribute the 3 to each term inside the parentheses: 3(8+11)=3×8+3×11
Multiply each term: 3×8=24 and 3×11=33. So 3(8+11)=24+33
Final Answer
24 + 33
Question 4HardMultiple Choice
A camp counselor packs 8 bags with 5 sandwiches and 3 fruit cups in each bag. Which expression uses the distributive property to find the total number of items?
Correct answer: C. 8(5+3)
This explanation shows one way to solve the problem.
Identify the structure: Each of the 8 bags contains two types of items: 5 sandwiches and 3 fruit cups
Apply the distributive property: Factor out the common number of bags: 8×5+8×3=8(5+3)
Final Answer
8(5 + 3)
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