Lesson 14: The Distributive Property6.AT.7

I can…

I can use the distributive property to expand and factor expressions.

Key words

• The Distributive Property — Multiply by each part inside the ( ).
• Distributive Property — Multiply by each part inside the ( ).
• Factor — A number that goes into a number with none left.
• Expand — Multiply so the ( ) are gone.
• Equivalent — The same value shown in a new way.
• Coefficient — The number in front of a letter, like 3 in 3x.
• Like terms — Terms with the same letter and the same power.

Steps

1. Each bundle has a ticket ($15) and a snack ($5). For 3 bundles I can write 3(15 + 5).
2. Way 1: add inside first. 15 + 5 = 20, then 3 × 20 = 60.
3. Way 2: distribute the 3 to each part. 3 × 15 + 3 × 5.
4. That is 45 + 15 = 60.
5. Both ways give $60, so 3(15 + 5) = 3 × 15 + 3 × 5.

Try it

Grandma packs 4 snack bags. Each bag has y grapes and 5 crackers, so the total is 4(y + 5). Which expression is equivalent to 4(y + 5)?

Check your answer

4y + 20

4(y + 5) = 4 × y + 4 × 5 = 4y + 20. The 4 must multiply BOTH terms — multiplying only the y gives 4y + 5, multiplying only the 5 gives y + 20, and adding 4 + 5 instead of multiplying gives 4y + 9.

Sentence starter

I know ___ because ___.

Goal: I can explain my steps using the words distributive property, factor, expand, and equivalent.