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Distributive Property Introduction

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Distributive Property Introduction

A snack stand packs the same number of crackers into two boxes. Use the distributive property to find totals and make multiplication easier. Show your thinking where asked.

Spot the shared factor

When the same number multiplies two addends, it can be factored out: a × b + a × c = a × (b + c).

1.At the stand, 4 bags have 6 crackers each and 4 bags have 3 crackers each. In 4 × 6 + 4 × 3, what is the common factor?

2.Choose the equation that correctly rewrites 5 × 7 + 5 × 2 using the distributive property.

5 × (7 + 2)
7 × (5 + 2)
5 + (7 × 2)
(5 × 7) + 2

3.True or false: 3 × 8 + 3 × 4 is equal to 3 × (8 + 4).

TrueFalse

Use the grouping shortcut

Factor out the shared number, then add inside the parentheses and multiply.

4.Find the total number of crackers in 5 × 6 + 5 × 2. Write both the factored expression and the total.

5.Rewrite 6 × 4 + 6 × 3 as one multiplication expression using parentheses. Then calculate the product.

6.A team sets out 8 plates with 4 apple slices on each plate and 8 plates with 5 orange slices on each plate. Write a distributive-property expression for the total number of slices, then find the total.

7.Mateo says 7 × 3 + 7 × 2 can be rewritten as 7 × (3 + 2). Is Mateo correct? Explain how you know.

8.A student rewrites 9 × 2 + 9 × 5 as 9 × (2 + 5), but then calculates 9 × 7 = 56. Identify the calculation mistake and give the correct total.

9.Write your own example of a sum with a shared factor, rewrite it using the distributive property, and find its value.