Multiplying fractions word problems

Multiplying fractions word problems arise in numerous situations. We will show you some examples.


I recommend that before starting this lesson, review multiplication of fractions  or  multiply fractions calculator

Example #1:
What is one-fourth of half?

Solution

You can probably model this problem with the following illustration:

Example #1:
What is one-fourth of half?

Solution

You can probably model this problem with the following illustration:

In the figure above, we broke it into half. Then, break half into 4 equal parts. The result?

The shaded area is one-eighth

You could solve the same problem simply by doing a multiplication of 1/4 and 1/2

1/4 × 1/2 = 1/8

In general,no need to make a graph to solve these type of problems

Just do multiplication!

Example #2
What is one-third of three-fourths?

Solution

1/3 × 3/4 = 3/12 = 1/4

If you want to model the situation, you will construct the following graph:

Example #3:
A recipe needs 1/4 tablespoon salt. How much salt does 8 such recipe need?

Solution

This word problem requires multiplication of fractions

Instead of adding 1/4 eight times, we can just do:

1/4 × 8 = 1/4 × 8/1 = 8/4 = 2

To make 8 recipes, we need 2 tablespoons of salt.

Exercises #4:
Peter's truck gets him 10 2/3 miles per gallon. Suppose Peter's tank is empty and he puts 5 1/2 gallons, how far can Peter go with the truck?

Solution

This word problem requires too multiplication. Also, Note that both numbers are mixed numbers. Thus, you have to convert them to improper fractions before you multiply.

10 2/3 × 5 1/2 = (10 × 3 + 2)/3 × (5 × 2 +1)/2 = 32/3 × 11/2

10 2/3 × 5 1/2 = (32 × 11)/6 = 352/6 = 58.66 miles