How to Solve Word Problems Involving Multiplying Mixed Numbers?

In this step-by-step guide, you will learn how to solve word problems involving multiplying mixed numbers.

A step-by-step guide to word problems involving multiplying mixed numbers

Mixed numbers have a whole number and a fraction.

To multiply mixed numbers, follow these steps:
Step 1: Write down the mixed number as an improper fraction.
Step 2: Multiply the numerators.
Step 3: Multiply the denominators.
Step 4: Simplify the product if possible.

Word Problem Involving Multiplying Mixed Numbers – Example 1

Daniel and Kevin made ladders. Daniel’s ladder is $$7$$ feet tall. Kevin’s ladder is $$2 \frac{3}{5}$$ times as tall as Daniel’s. How tall is Kevin’s ladder?

Solution:

Since the Kevin’s ladder is $$2 \frac{3}{5}$$ times as tall as Daniel’s, multiply $$2 \frac{3}{5}$$ in $$7$$.

$$2 \frac{3}{5}×7=$$?, $$2 \frac{3}{5}=\frac{(2×5)+3}{5}=\frac{13}{5}$$

Write $$7$$ as an improper fraction. $$\frac{7}{1}$$

Multiply the numerators and the denominators. $$\frac{13}{5}×\frac{7}{1}=\frac{91}{5}$$

Simplify and write as a mixed number. $$\frac{91}{5}=18 \frac{1}{5}$$

Word Problem Involving Multiplying Mixed Numbers – Example 2

An office is $$16 \frac{2}{3}$$ yards wide. Its length is $$4 \frac{1}{4}$$ times as long as it is wide. How long is the length of the office?

Solution:

Since the length is $$4 \frac{1}{4}$$ times as long as $$16 \frac{2}{3}$$, multiply $$4 \frac{1}{4}$$ in $$16 \frac{2}{3}$$.

$$4 \frac{1}{4}×16 \frac{2}{3}=$$?, $$4 \frac{1}{4}=\frac{(4×4)+1}{4}=\frac{17}{4}, 16 \frac{2}{3}=\frac{(16×3)+2}{3}=\frac{50}{3}$$

Multiply the numerators and the denominators. $$\frac{17}{4}×\frac{50}{3}=\frac{850}{12}$$

Simplify and write as a mixed number. $$\frac{850}{12}=70 \frac{10}{12}=70 \frac{5}{6}$$

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