Division with Fractions

Section 7.3 Dividing by a fraction can be thought about as repeated subtraction or sharing equally.

1/2 divided by 3/4 can be read as:

(a) Repeated subtraction: How much of the three-fourths are in a half? To model this, you would start with the ½ and subtract two-thirds of the ¾.

(b) Equal share: If three-quarters gets a half, how much would a whole get? To model this you would first consider how much of the half is equally distributed in each of the three quarters (each qtr gets 1/6), then using that equal share you can determine how much is in the whole (4/6 = 2/3).

Here are some sample word problems (from 7.3 #15) that use fractions for division.

Repeated subtraction:
15a. If a tortoise is timed traveling an average of 1 2/3 miles per hour, how long would it take the tortoise to travel 6 miles?

15a. The recipe you use to make holiday cookies uses 1 2/3 cups of flour for each batch of cookies. How many batches of cookies can you make with the 6 cups of flour.

15b. How many 2 ¾ feet long strips of ribbon can be cut from a ribbon that is 7 ½ feet long?

15b. If your pea patch is only 7 ½ square yards and the melon plants you want to grow require 2 ¾ square yards each. How many melon plants can you put into your pea patch? Show your work and explain your reasoning.

Sharing Equally:
15b. You have 7 ½ bags of mulch to cover 2 ¾ square yards of garden bed. If you want to distribute the mulch evenly over the garden bed, how many bags will you need to use for each square yard?

15c. If you want to share1 7/8 pizza with 3 people, how much pizza would each person get?