# 6.9 Combinations of operations with decimals and fractions

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses combinations of operations with decimals and fractions. By the end of the module students should be able to combine operations with decimals.

Having considered operations with decimals and fractions, we now consider opera­tions that involve both decimals and fractions.

## Sample set a

Perform the following operations.

$0\text{.}\text{38}\cdot \frac{1}{4}$ . Convert both numbers to decimals or both numbers to fractions. We’ll convert to decimals.

To convert $\frac{1}{4}$ to a decimal, divide 1 by 4.

Now multiply 0.38 and .25.

Thus, $0\text{.}\text{38}\cdot \frac{1}{4}=0\text{.}\text{095}$ .

In the problems that follow, the conversions from fraction to decimal, or decimal to fraction, and some of the additions, subtraction, multiplications, and divisions will be left to you.

$1\text{.}\text{85}+\frac{3}{8}\cdot 4\text{.}1$ Convert $\frac{3}{8}$ to a decimal.

$1\text{.}\text{85}+0\text{.}\text{375}\cdot 4\text{.}1$ Multiply before adding.

$1\text{.}\text{85}+1\text{.}\text{5375}$ Now add.

3.3875

$\frac{5}{\text{13}}\left(\frac{4}{5}-0\text{.}\text{28}\right)$ Convert 0.28 to a fraction.

$\begin{array}{ccc}\frac{5}{\text{13}}\left(\frac{4}{5}-\frac{\text{28}}{\text{100}}\right)& =& \frac{5}{\text{13}}\left(\frac{4}{5}-\frac{7}{\text{25}}\right)\hfill \\ & =& \frac{5}{\text{13}}\left(\frac{\text{20}}{\text{25}}-\frac{7}{\text{25}}\right)\hfill \\ & =& \frac{\stackrel{1}{\overline{)5}}}{\underset{1}{\overline{)13}}}\cdot \frac{\stackrel{1}{\overline{)13}}}{\underset{5}{\overline{)25}}}\hfill \\ & =& \frac{1}{5}\hfill \end{array}$

$\begin{array}{cccc}\frac{0.125}{1\frac{1}{3}}+\frac{1}{16}-0.1211& =& \frac{\frac{125}{1000}}{\frac{4}{3}}+\frac{1}{16}-0.1211\hfill & \\ & =& \frac{\frac{1}{8}}{\frac{4}{3}}+\frac{1}{16}-0.1211\hfill & \\ & =& \frac{1}{8}\cdot \frac{3}{4}+\frac{1}{16}-0.1211\hfill & \\ & =& \frac{3}{32}+\frac{1}{16}-0.1211\hfill & \\ & =& \frac{3}{32}+\frac{2}{32}-0.1211=\frac{5}{32}-0.1211\hfill & \\ & =& 0.15625-0.1211\hfill & \\ & =& 0.03515\hfill & \text{Convert this to fraction form}\hfill \\ & =& \frac{3515}{100,000}\hfill & \\ & =& \frac{703}{20,000}\hfill & \end{array}$

## Practice set a

Perform the following operations.

$\frac{3}{5}+1\text{.}6$

2.2 or $2\frac{1}{5}$

$8\text{.}\text{91}+\frac{1}{5}\cdot 1\text{.}6$

9.23

$1\frac{9}{\text{16}}\left(6\text{.}\text{12}+\frac{7}{\text{25}}\right)$

10

$\frac{0\text{.}\text{156}}{1\frac{\text{11}}{\text{15}}}-0\text{.}\text{05}$

## Exercises

$\frac{3}{\text{10}}+0\text{.}7$

1

$\frac{1}{5}+0\text{.}1$

$\frac{5}{8}-0\text{.}\text{513}$

0.112

$0\text{.}\text{418}-\frac{\text{67}}{\text{200}}$

$0\text{.}\text{22}\cdot \frac{1}{4}$

0.055

$\frac{3}{5}\cdot 8\text{.}4$

$\frac{1}{\text{25}}\cdot 3\text{.}\text{19}$

0.1276

0.7

$9\text{.}\text{26}+\frac{1}{4}\cdot 0\text{.}\text{81}$

9.4625

$0\text{.}\text{588}+\frac{1}{\text{40}}\cdot 0\text{.}\text{24}$

$\frac{1}{\text{20}}+3\text{.}\text{62}\cdot \frac{3}{8}$

1.4075

$\frac{\text{15}}{\text{16}}\cdot \left(\frac{7}{\text{10}}-0\text{.}5\right)$

0.1875

$0\text{.}2\cdot \left(\frac{7}{\text{20}}+1\text{.}\text{1143}\right)$

$\frac{3}{4}\cdot \left(0\text{.}\text{875}+\frac{1}{8}\right)$

0.75

$5\text{.}\text{198}-0\text{.}\text{26}\cdot \left(\frac{\text{14}}{\text{250}}+0\text{.}\text{119}\right)$

$0\text{.}5\frac{1}{4}+{\left(0\text{.}3\right)}^{2}$

0.615

${\left(1\text{.}4\right)}^{2}-1\text{.}6\frac{1}{2}$

${\left(\frac{3}{8}\right)}^{2}-0\text{.}\text{000625}+\left(1\text{.}1{\right)}^{2}$

1.35

${\left(0\text{.}6\right)}^{2}\cdot \left(\frac{1}{\text{20}}-\frac{1}{\text{25}}\right)$

${\left(\frac{1}{2}\right)}^{2}-0\text{.}\text{125}$

0.125

$\frac{0\text{.}\text{75}}{4\frac{1}{2}}+\frac{5}{\text{12}}$

$\left(\frac{0\text{.}\text{375}}{2\frac{1}{\text{16}}}-\frac{1}{\text{33}}\right)$

$0\text{.}\overline{\text{15}}$

$8\frac{1}{3}\cdot \left(\frac{1\frac{1}{4}}{2\text{.}\text{25}}+\frac{9}{\text{25}}\right)$

$\frac{\frac{0\text{.}\text{32}}{\frac{\text{12}}{\text{35}}}}{0\text{.}\text{35}}$

$2\text{.}\overline{6}$

$\frac{\left(\sqrt{\frac{49}{64}}-5\right)0.125}{1.375}$

## Exercises for review

( [link] ) Is 21,480 divisible by 3?

yes

( [link] ) Expand ${14}^{4}$ . Do not find the actual value.

( [link] ) Find the prime factorization of 15,400.

${2}^{3}\cdot {5}^{2}\cdot 7\cdot 11$

( [link] ) Convert 8.016 to a fraction.

( [link] ) Find the quotient. $\text{16}÷\text{27}$ .

$0\text{.}\overline{\text{592}}$

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