Fractions Outside the Parentheses

Hand out a fraction

When the number outside the parentheses is a fraction, it still multiplies every term inside. Use the shortcut from Unit 3: to take a fraction of a number, divide by the bottom first, then multiply by the top.

12(6x + 10)12 × 6x + 12 × 10 hand it to every term3x + 5

34(8x − 12)34(8x + ⁻12) adding the opposite8 ÷ 4 = 2 and 2 × 3 = 6; ⁻12 ÷ 4 = ⁻3 and ⁻3 × 3 = ⁻9 divide by the bottom, then multiply by the top6x − 9

⁻23(9y − 6)⁻23 × 9y + ⁻23 × (⁻6) hand it to every term⁻6y + 4

What value of k makes ⁻10.5x + k and ⁻2.1(5x − 3.7) + 4.1 equivalent?

⁻2.1(5x − 3.7) + 4.1⁻10.5x + 7.77 + 4.1 expand⁻10.5x + 11.87so k = 11.87

The x parts already match, so k has to match the number part.

Elle and Finn

ElleMath-speak

The distributive property holds for all rational numbers, so a fraction outside the parentheses multiplies each term inside.

FinnPlain English

Fractions get handed out too. Take that fraction of every term inside.

Elle and Finn talk it over

Finn

Half of everything? Can I have half the cookies?

Elle

You get half of every pile. Half the chocolate chip, half the oatmeal.

Finn

So 12(6x + 10) is 3x + 5 cookies.

Elle

That's exactly it. Nobody's pile gets skipped.

Let me try a few

NC standards: NC.7.EE.1, NC.7.NS.2.

Where to go next

Let me try a few7 problems on fractions outside the parentheses. All tilesAll 3 parts of this lesson. Tell us what you thought about this tileA few quick questions about just this tile. It takes a few minutes, and opens in a new tab so you keep your place.