Multiplying Mixed Numbers Word Problems

Concept

A mixed number is one that combines an integer and a fraction. They can be expressed initially as improper fractions and then broken down into their mixed number form.

Rules

1. Change all the mixed numbers to improper fractions.
2. Reduce the fractions.
3. Cross out any common factors.
4. Multiply the numerators together and the denominators together.
5. Reduce the answer.

Example

Donald ate $\fn_phv {\color{Teal} 3\frac{2}{3}}$ pizza in a week. Liam ate $\fn_phv {\color{Teal} 2\frac{1}{4}}$ times that amount in a week. How much pizza did Liam eat?

Solution

Change each mixed number to an improper fraction.
$\fn_phv 3\frac{2}{3}={\color{Red} \frac{11}{3}}$ $\fn_phv 2\frac{1}{4}={\color{Red} \frac{9}{4}}$
Multiply and reduce the answer to lowest terms.
Divide by 3: $\fn_phv \frac{11}{3{\color{Red} \div 3}}\times \frac{9{\color{Red} \div 3}}{4} = \frac{11}{\color{Red} 1}\times \frac{\color{Red} 3}{4}$
Multiply the fractions.
$\fn_phv \frac{11}{\color{Red} 1}\times \frac{\color{Red} 3}{4}=\frac{3\times 11}{1\times 4}=\frac{\color{Red} 33}{4}$
Rewrite the answer as a mixed number if possible.
Answer: $\fn_phv \frac{33}{4}={\color{Red} 8\frac{1}{4}}$ pizzas

Practice Multiplying Mixed Numbers Word Problems

Practice Problem 1

Sam’s rabbit weighs $\fn_phv {\color{Teal} 3\frac{1}{2}}$ kilograms. Zander’s rabbit weighs $\fn_phv {\color{Teal} 1\frac{1}{2}}$ times as much as Sam’s. How much does Zander’s rabbit weigh?
Write the product as a whole number or a fraction or a mixed number in the simplest form.

Practice Problem 2

A fruit farm is $\fn_phv {\color{Teal} 4\frac{1}{2}}$ kilometers wide. Its length is $\fn_phv {\color{Teal} 3\frac{2}{3}}$ times as long as it is wide. What is the area of the farm?
Write the product as a whole number or a fraction or a mixed number in the simplest form.

Practice Problem 3

A small tank contains $\fn_phv {\color{Teal} 5\frac{1}{3}}$ liters of water. The capacity of a large tank is 6 times more than the small tank. What’s the capacity of the large tank?
Write the product as a whole number or a fraction or a mixed number in the simplest form.