Combining Like Terms – Sorting Letters

Did you ever play sorting games as a little kid? If you fold your own laundry, then you should be a pro at sorting – pants, shirts, socks, sweaters.

Combing like terms is just like sorting laundry, or marbles (as illustrated in my sorry attempt at drawing marbles).

When we have “letters” (also known as variables) in an expression we often want to combine them so that we have an easier expression to look at.

Think of it like having a pile full of different color marbles (like in the illustration above). Let’s look at an example:

2x + 4y – 3xy + 7y – 5x + 2xy

Let’s look at the different “color” marbles we have (that is, the different “terms”)

We have x’s, y’s, and xy’s (the xy’s are their own type of term, because xy is not the same as x or y).

Now we combine the things that are “like” – We have 2x and –5x, so that is –3x. We have 4y and 7y, so that is 11y. Finally, we have –3xy and 2xy, which is –xy.

Our “simplified” expression is –3x +11y –xy.

Because of the commutative property of addition, we can write the expression in any order we want to.

-3x – xy + 11y
11y – 3x – xy

etc, etc

Here are some practice problems for combining like terms (also known as “simplifying expressions”)

Simplify the Expressions by combining like terms

1.

2.

3.

4.

5.

(Pre-Math Tip! Play sorting games with your preschooler. You may not realize it now when you are sorting blocks and dishes and beads, but your preschooler is building the foundation for basic algebra skills like being able to combine like terms!)

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