More Than One Kind · Deep Dive 5

x's, y's, and plain numbers

Some expressions have two different variables, like x and y. They are different kinds of pieces, so they never combine with each other. Sort them into piles first: the x pile, the y pile, and the number pile. Then count each pile.

3x + 2y − x + 5y − 43x + 2y + ⁻1x + 5y + ⁻4 marked, adding the opposite

Circles are x terms. Triangles are y terms. Boxes are constants. The shape says which is which, not the colour.

Sorted into three piles:

x pile: 3x + ⁻1xy pile: 2y + 5ynumber pile: ⁻4

Elle and Finn

ElleMath-speak

Like terms have exactly the same variable part. Terms with different variables are unlike terms, and they stay separate.

FinnPlain English

x's go with x's, y's go with y's, and plain numbers go with plain numbers. You can't add apples to bananas.

Elle and Finn talk it over

Finn

So 3x + 2y is 5xy?

Elle

No. That's like saying 3 apples plus 2 bananas is 5 apple-bananas.

Finn

I would eat an apple-banana.

Elle

It still stays 3x + 2y.

3x + 2y is already as simple as it gets. Unlike terms are left just as they are.

Watch it work

3x + 2y − x + 5y − 43x + 2y + ⁻1x + 5y + ⁻4 adding the opposite, invisible 1(3x + ⁻1x) + (2y + 5y) + ⁻4 move like terms together2x + 7y − 4

6a − 2b + 3 − 6a + b6a + ⁻2b + 3 + ⁻6a + 1b adding the opposite, invisible 1(6a + ⁻6a) + (⁻2b + 1b) + 3 move like terms together0a + ⁻1b + 3⁻b + 3

0a is 0, so the a terms disappear, and ⁻1b is written ⁻b.

Let me try a few

NC standard: NC.7.EE.1.

Where to go next

Let me try a few6 problems on more than one kind. Next: Tile 2, Adding ExpressionsPut the two piles together 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.