~ 4.4 ~

Using the distributive property provides a shortcut for calculating the final amount in situations that involve adding or subtracting a fraction of the original amount.

For example, one day Clare runs 4 miles. The next day, she plans to run that same distance plus half as much again. How far does she plan to run the next day?

Tomorrow she will run 4 miles plus ½ of 4 miles. We can use the distributive property to find this in one step:

1 ⋅ 4 + ½ ⋅ 4 = (1 + ½) ⋅ 4

Clare plans to run 1 ½ ⋅ 4, or 6 miles.

This works when we decrease by a fraction, too. If Tyler spent x dollars on a new shirt, and Noah spent 13 less than Tyler, then Noah spent ⅔ x dollars since x − ⅓ x = ⅔ x.