The phrases “combine like terms” or “collect like terms” are used a lot in algebra, and for good reason. The process they describe is used a lot in solving algebra problems. Two approaches, one intuitive and the other algebraic, can help in understanding why some terms are “like” terms, and others are not.

### Quantities With Units

Suppose you are sitting in front of a table that holds three piles of fruit:

– five apples

– three oranges

– four apples

If someone asks you “What do you see on the table?”, how would you answer the question?

Chances are you answered “nine apples and three oranges”. Why did you combine the two piles of apples with one another, but not with the oranges? How did you know that you could do that?

The quantities of apples may be combined because addition or subtraction only work with quantities that have the same units, such as apples in the example above. If you were asked to add three apples and two oranges, the only answer you could give is “three apples and two oranges”, since neither addition nor subtraction make sense with quantities that have differing units. The concepts of addition and subtraction are based on combining or separating quantities with the same units.

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