Negatives Get a Turn Too

Minus signs inside and outside

When there's subtraction inside, change it to adding the opposite first, like Lesson 1, Tile 2. When the number outside is negative, it multiplies every term inside too, and the signs follow the rules from Unit 3: same signs, positive, and different signs, negative.

3(2x − 5)3(2x + ⁻5) adding the opposite3 × 2x + 3 × (⁻5) hand it to every term6x + ⁻156x − 15

⁻4(x + 3)⁻4 × x + ⁻4 × 3 hand it to every term⁻4x + ⁻12⁻4x − 12

⁻2(3y − 7)⁻2(3y + ⁻7) adding the opposite⁻2 × 3y + ⁻2 × (⁻7) hand it to every term⁻6y + 14

⁻2 times ⁻7 is positive 14. Same signs, positive.

Elle and Finn

ElleMath-speak

When distributing a negative factor, multiply each term by the negative number. The sign of each product follows the rules for multiplying signed numbers.

FinnPlain English

A negative out front flips the sign of every term inside. Positive terms turn negative, and negative terms turn positive.

Elle and Finn talk it over

Finn

A negative out front is like a grumpy cookie hander.

Elle

How so?

Finn

Every kid still gets a cookie. But now the cookie is sad.

Elle

And the kids who were already sad?

Finn

Two sads make a happy. Unit 3 told me.

Elle

Only because we are multiplying.

That is real math. ⁻2(3y − 7) = ⁻6y + 14, because ⁻2 × (⁻7) = 14.

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 negatives get a turn too. Next: Tile 3, Expand, Then CombineTwo moves, one line at a time 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.