Math 7 · Unit 4, Lesson 1: Hand It Out, Take It Back · Tile 3 of 3
Combining Like Terms
Write in the invisible ones, then count what you have
Finn reads this
Once every piece is being added, combining is just counting. The trick is seeing which pieces are the same kind.
Write it down. Do every change on paper, one line per step. Changing signs in your head is the number one reason for missed problems. If you changed something, it should be on the paper.
The words
| Elle (math-speak) | Finn (plain English) |
|---|---|
| Term | A piece being added. |
| Coefficient | The number stuck to the front of the variable. In 7x, it is 7. |
| Constant | A number with no variable. The term never changes. That is why we call it constant. |
| Like terms | Terms with the exact same variable part. 4x and −2x are like terms. 4x and 4 are not. 3x and 3y are not. |
Write in the invisible ones
x means 1x (identity property: multiplying by 1 changes nothing)−x means −1xthe first term has an invisible + in front: 5x − 3 is +5x + −3−(x + 2) means −1(x + 2)x/3 means 13 x
Why combining works
Finn reads this
Combining like terms is undistributing the variable.
4x + 2x = (4 + 2)x = 6x
Four x's and two x's make six x's, the same way 4 cookies and 2 cookies make 6 cookies.
The steps, the same every time
Finn reads this
- Change subtraction to adding the opposite.
- Write in the invisible 1s.
- Mark like terms: circle the variable terms, box the constants.
- Move like terms together (commutative and associative properties).
- Add the coefficients. Keep the variable part the same.
- Tidy: write + −3 as − 3.
Worked example
5x − 3 + x − 4x + 95x + −3 + 1x + −4x + 9 adding the opposite5x + 1x + −4x + −3 + 9 commutative property(5x + 1x + −4x) + (−3 + 9) associative property(5 + 1 + −4)x + 6 distributive property2x + 6 add the coefficients
Circles are variable terms. Boxes are constants. The shape says which is which, not the colour.
NC standards: NC.7.EE.1.