# 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

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
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Salomon
I got X =-6
Salomon
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oops. ignore that.
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