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To add or subtract mixed numbers, convert each mixed number to an improper fraction, then add or subtract the resulting improper fractions.
Find the following sums and differences.
$8\frac{3}{5}+5\frac{1}{4}$ . Convert each mixed number to an improper fraction.
$8\frac{3}{5}=\frac{5\cdot 8+3}{5}=\frac{\text{40}+3}{5}=\frac{\text{43}}{5}$
$5\frac{1}{4}=\frac{4\cdot 5+1}{4}=\frac{\text{20}+1}{4}=\frac{\text{21}}{4}$ Now add the improper fractions $\frac{\text{43}}{5}\text{and}\frac{\text{21}}{4}$ .
$\frac{43}{5}+\frac{21}{4}$ The LCD = 20.
$\begin{array}{cccc}\hfill \frac{\text{43}}{5}+\frac{\text{21}}{4}& =& \frac{\text{43}\cdot 4}{\text{20}}+\frac{\text{21}\cdot 5}{\text{20}}\hfill & \\ & =& \frac{\text{172}}{\text{20}}+\frac{\text{105}}{\text{20}}\hfill & \\ & =& \frac{\text{172}+\text{105}}{\text{20}}\hfill & \\ & =& \frac{\text{277}}{\text{20}}\hfill & \text{Convert this improper fraction to a mixed number.}\\ & =& \text{13}\frac{\text{17}}{\text{20}}\hfill & \end{array}$
Thus, $8\frac{3}{5}+5\frac{1}{4}=\text{13}\frac{\text{17}}{\text{20}}$ .
$3\frac{1}{8}-\frac{5}{6}$ . Convert the mixed number to an improper fraction.
$3\frac{1}{8}=\frac{3\cdot 8+1}{8}=\frac{\text{24}+1}{8}=\frac{\text{25}}{8}$
$\frac{\text{25}}{8}-\frac{5}{6}$ The LCD = 24.
$\begin{array}{cccc}\hfill \frac{\text{25}}{8}-\frac{5}{6}& =& \frac{\text{25}\cdot 3}{\text{24}}-\frac{5\cdot 4}{\text{24}}\hfill & \\ & =& \frac{\text{75}}{\text{24}}-\frac{\text{20}}{\text{24}}\hfill & \\ & =& \frac{\text{75}-\text{20}}{\text{24}}\hfill & \\ & =& \frac{\text{55}}{\text{24}}\hfill & \text{Convert his improper fraction to a mixed number.}\hfill \\ & =& 2\frac{7}{\text{24}}\hfill & \end{array}$
Thus, $3\frac{1}{8}-\frac{5}{6}=2\frac{7}{\text{24}}$ .
Find the following sums and differences.
$\text{16}+2\frac{9}{\text{16}}$
$\text{18}\frac{9}{\text{16}}$
For the following problems, perform each indicated operation.
$5\frac{1}{3}+6\frac{1}{3}$
$\text{10}\frac{5}{\text{12}}+2\frac{1}{\text{12}}$
$\text{12}\frac{1}{2}$
$\text{15}\frac{1}{5}-\text{11}\frac{3}{5}$
$9\frac{3}{\text{11}}+\text{12}\frac{3}{\text{11}}$
$\text{21}\frac{6}{\text{11}}$
$1\frac{1}{6}+3\frac{2}{6}+8\frac{1}{6}$
$\frac{3}{5}+5\frac{1}{5}$
$6+\text{11}\frac{2}{3}$
$\text{17}-8\frac{3}{\text{14}}$
$8\frac{\text{11}}{\text{14}}$
$5\frac{1}{3}+2\frac{1}{4}$
$8\frac{2}{5}+4\frac{1}{\text{10}}$
$1\frac{1}{3}+\text{12}\frac{3}{8}$
$\text{13}\frac{\text{17}}{\text{24}}$
$3\frac{1}{4}+1\frac{1}{3}-2\frac{1}{2}$
$4\frac{3}{4}-3\frac{5}{6}+1\frac{2}{3}$
$\text{2}\frac{7}{12}$
$3\frac{1}{\text{12}}+4\frac{1}{3}+1\frac{1}{4}$
$5\frac{1}{\text{15}}+8\frac{3}{\text{10}}-5\frac{4}{5}$
$7\frac{\text{17}}{\text{30}}$
$7\frac{1}{3}+8\frac{5}{6}-2\frac{1}{4}$
$\text{19}\frac{\text{20}}{\text{21}}+\text{42}\frac{6}{7}-\frac{5}{\text{14}}+\text{12}\frac{1}{7}$
$\text{74}\frac{\text{25}}{\text{42}}$
$\frac{1}{\text{16}}+4\frac{3}{4}+\text{10}\frac{3}{8}-9$
$\text{11}-\frac{2}{9}+\text{10}\frac{1}{3}-\frac{2}{3}-5\frac{1}{6}+6\frac{1}{\text{18}}$
$\text{21}\frac{1}{3}$
$\frac{5}{2}+2\frac{1}{6}+\text{11}\frac{1}{3}-\frac{\text{11}}{6}$
$1\frac{1}{8}+\frac{9}{4}-\frac{1}{\text{16}}-\frac{1}{\text{32}}+\frac{\text{19}}{8}$
$5\frac{\text{21}}{\text{32}}$
$\text{22}\frac{3}{8}-\text{16}\frac{1}{7}$
$\text{15}\frac{4}{9}+4\frac{9}{\text{16}}$
$\text{20}\frac{1}{\text{144}}$
$4\frac{\text{17}}{\text{88}}+5\frac{9}{\text{110}}$
$6\frac{\text{11}}{\text{12}}+\frac{2}{3}$
$7\frac{7}{\text{12}}$
$8\frac{9}{\text{16}}-\frac{7}{9}$
$5\frac{2}{\text{11}}-\frac{1}{\text{12}}$
$5\frac{\text{13}}{\text{132}}$
$\text{18}\frac{\text{15}}{\text{16}}-\frac{\text{33}}{\text{34}}$
$1\frac{\text{89}}{\text{112}}-\frac{\text{21}}{\text{56}}$
$1\frac{\text{47}}{\text{212}}$
$\text{11}\frac{\text{11}}{\text{24}}-7\frac{\text{13}}{\text{18}}$
$5\frac{\text{27}}{\text{84}}-3\frac{5}{\text{42}}+1\frac{1}{\text{21}}$
$3\frac{1}{4}$
$\text{16}\frac{1}{\text{48}}-\text{16}\frac{1}{\text{96}}+\frac{1}{\text{144}}$
A man pours $2\frac{5}{8}$ gallons of paint from a bucket into a tray. After he finishes pouring, there are $1\frac{1}{4}$ gallons of paint left in his bucket. How much paint did the man pour into the tray?
$2\frac{5}{8}\phantom{\rule{4px}{0ex}}\text{gallons}$
A particular computer stock opened at $\text{37}\frac{3}{8}$ and closed at $\text{38}\frac{1}{4}$ . What was the net gain for this stock?
A particular diet program claims that $4\frac{3}{\text{16}}$ pounds can be lost the first month, $3\frac{1}{4}$ pounds can be lost the second month, and $1\frac{1}{2}$ pounds can be lost the third month. How many pounds does this diet program claim a person can lose over a 3-month period?
$8\frac{15}{16}\phantom{\rule{4px}{0ex}}\text{pounds}$
If a person who weighs $\text{145}\frac{3}{4}$ pounds goes on the diet program described in the problem above, how much would he weigh at the end of 3 months?
If the diet program described in the problem above makes the additional claim that from the fourth month on, a person will lose $1\frac{1}{8}$ pounds a month, how much will a person who begins the program weighing $\text{208}\frac{3}{4}$ pounds weight after 8 months?
$194\frac{3}{16}\phantom{\rule{4px}{0ex}}\text{pounds}$
( [link] ) Use exponents to write $4\cdot 4\cdot 4$ .
( [link] ) Convert $\frac{\text{16}}{5}$ to a mixed number.
( [link] ) Find the sum. $\frac{4}{9}+\frac{1}{9}+\frac{2}{9}$ .
$\frac{7}{9}$
( [link] ) Find the difference. $\frac{\text{15}}{\text{26}}-\frac{3}{\text{10}}$ .
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