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})

Pre-Algebra for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

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})