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. \(\frac{850}{12}=70 \frac{10}{12}=70 \frac{5}{6}\)