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.

The first two examples will show you how to model the problem with a figure.

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. What is the result?

The shaded area is one-eighth of the entire figure.

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

1/4 × 1/2 = (1 × 1)/(2 × 4) = 1/8

In general, there is no need to make a graph to solve these types of problems. You can 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:



In the figure above, we used a blue line to represent three-fourths. Then, we broke three-fourths into 3 equal parts. What is the result? The shaded area or 1 part of the three-fourths is one-fourth of the entire figure.

Multiplying fractions word problems: How to do this without a figure or an illustration

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 the following:

1/4 × 8 = 1/4 × 8/1 = (1 × 8)/(4 × 1) = 8/4 = 2

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

Example #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 perform the multiplication.

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

10 2/3 × 5 1/2 = (30 + 2)/3 × (10 + 1)/2

10 2/3 × 5 1/2 = 32/3 × 11/2

10 2/3 × 5 1/2 = (32 × 11)/(3 × 2)

10 2/3 × 5 1/2 = 352/6 = 58.66 miles

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