Division by Fractions

Section 7.3
Dividing by a fraction can be thought about as repeated subtraction (a/b means how many ‘b’s or how much of ‘b’ is in ‘a’) or sharing equally (a/b means how much of ‘a’ does each ‘b’ get).

1/2 divided by 3/4 can be read as: (a) Repeated subtraction: How much of the three-fourths is in a half? To model this, consider the ½ as your whole and ask yourself what part of ¾ is in that whole. We know that two of the fourths is in the half, and those two fourths are 2/3 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:
· 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?
· Your holiday cookie recipe 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?
· How many 2 ¾ feet long strips of ribbon can be cut from a ribbon that is 7 ½ feet long?
· 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?

Sharing Equally:
· 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?
· If you want to share 1 7/8 pizza with 3 people, how much pizza would each person get?
· If you have 3 donuts in 1/3 of a box, how many donuts are in a whole box?