# 1.12 Fractions: multiplication of mixed numerals

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses multiplication of fractions. By the end of the module students should be able to understand the concept of multiplication of fractions, multiply one fraction by another, multiply mixed numbers and find powers and roots of various fractions.

## Section overview

• Multiplication of Mixed Numbers

## Multiplying mixed numbers

To perform a multiplication in which there are mixed numbers, it is convenient to first convert each mixed number to an improper fraction, then multiply.

## Sample set c

Perform the following multiplications. Convert improper fractions to mixed numbers.

$1\frac{1}{8}\cdot 4\frac{2}{3}$

Convert each mixed number to an improper fraction.

$1\frac{1}{8}=\frac{8\cdot 1+1}{8}=\frac{9}{8}$

$4\frac{2}{3}=\frac{4\cdot 3+2}{3}=\frac{\text{14}}{3}$

$\frac{\stackrel{3}{\overline{)9}}}{\underset{4}{\overline{)8}}}\cdot \frac{\stackrel{7}{\overline{)14}}}{\underset{1}{\overline{)3}}}=\frac{3\cdot 7}{4\cdot 1}=\frac{\text{21}}{4}=5\frac{1}{4}$

$\text{16}\cdot 8\frac{1}{5}$

Convert $8\frac{1}{5}$ to an improper fraction.

$8\frac{1}{5}=\frac{5\cdot 8+1}{5}=\frac{\text{41}}{5}$

$\frac{16}{1}\cdot \frac{41}{5}$ .

There are no common factors to divide out.

$\frac{\text{16}}{1}\cdot \frac{\text{41}}{5}=\frac{\text{16}\cdot \text{41}}{1\cdot 5}=\frac{\text{656}}{5}=\text{131}\frac{1}{5}$

$9\frac{1}{6}\cdot \text{12}\frac{3}{5}$

Convert to improper fractions.

$9\frac{1}{6}=\frac{6\cdot 9+1}{6}=\frac{\text{55}}{6}$

$\text{12}\frac{3}{5}=\frac{5\cdot \text{12}+3}{5}=\frac{\text{63}}{5}$

$\frac{\stackrel{\text{11}}{\overline{)55}}}{\underset{2}{\overline{)6}}}\cdot \frac{\stackrel{\text{21}}{\overline{)63}}}{\underset{1}{\overline{)5}}}=\frac{\text{11}\cdot \text{21}}{2\cdot 1}=\frac{\text{231}}{2}=\text{115}\frac{1}{2}$

$\begin{array}{ccc}\hfill \frac{11}{8}\cdot 4\frac{1}{2}\cdot 3\frac{1}{8}& =& \frac{11}{8}\cdot \frac{\stackrel{3}{\overline{)9}}}{\underset{1}{\overline{)2}}}\cdot \frac{\stackrel{5}{\overline{)10}}}{\underset{1}{\overline{)3}}}\hfill \\ & =& \frac{11\cdot 3\cdot 5}{8\cdot 1\cdot 1}=\frac{165}{8}=20\frac{5}{8}\hfill \end{array}$

## Practice set c

Perform the following multiplications. Convert improper fractions to mixed numbers.

$2\frac{2}{3}\cdot 2\frac{1}{4}$

6

$6\frac{2}{3}\cdot 3\frac{3}{\text{10}}$

22

$7\frac{1}{8}\cdot \text{12}$

$\text{85}\frac{1}{2}$

$2\frac{2}{5}\cdot 3\frac{3}{4}\cdot 3\frac{1}{3}$

30

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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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