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the sum of $\mathrm{-4}$ and $\mathrm{-17}$ , increased by 32
$\left(\mathrm{-4}+\left(\mathrm{-17}\right)\right)+32;11$
ⓐ the difference of 15 and $\mathrm{-7}$ ⓑ subtract 15 from $\mathrm{-7}$
the quotient of $\mathrm{-45}$ and $\mathrm{-9}$
$\frac{\mathrm{-45}}{\mathrm{-9}};5$
the product of $\mathrm{-12}$ and the difference of $c\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}d$
Use Integers in Applications
In the following exercises, solve.
Temperature The high temperature one day in Miami Beach, Florida, was $76\text{\xb0}$ . That same day, the high temperature in Buffalo, New York was $\text{\u2212}8\text{\xb0}$ . What was the difference between the temperature in Miami Beach and the temperature in Buffalo?
84 degrees
Checking Account Adrianne has a balance of $\text{\u2212}\mathrm{\$22}$ in her checking account. She deposits $301 to the account. What is the new balance?
Find Equivalent Fractions
In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
$\frac{1}{4}$
$\frac{2}{8},\frac{3}{12},\frac{4}{16}$ answers may vary
$\frac{1}{3}$
$\frac{5}{6}$
$\frac{10}{12},\frac{15}{18},\frac{20}{24}$ answers may vary
$\frac{2}{7}$
Simplify Fractions
In the following exercises, simplify.
$\frac{8}{24}$
$\frac{12}{18}$
$-\phantom{\rule{0.2em}{0ex}}\frac{168}{192}$
$-\phantom{\rule{0.2em}{0ex}}\frac{7}{8}$
$-\phantom{\rule{0.2em}{0ex}}\frac{140}{224}$
$\frac{15a}{15b}$
Multiply Fractions
In the following exercises, multiply.
$\frac{1}{2}\xb7\frac{3}{8}$
$\frac{7}{12}\left(-\phantom{\rule{0.2em}{0ex}}\frac{8}{21}\right)$
$-\phantom{\rule{0.2em}{0ex}}\frac{2}{9}$
$\frac{5}{12}\left(-\phantom{\rule{0.2em}{0ex}}\frac{8}{15}\right)$
$\mathrm{-28}p\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}\right)$
$7p$
$\mathrm{-51}q\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}\right)$
$\mathrm{-1}\left(-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}\right)$
Divide Fractions
In the following exercises, divide.
$\frac{1}{2}\xf7\frac{1}{8}$
$-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}\xf7\frac{4}{7}$
$-\phantom{\rule{0.2em}{0ex}}\frac{7}{5}$
$-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}\xf7\frac{3}{5}$
$\frac{5}{6}\xf7\frac{c}{15}$
$\frac{5q}{12}\xf7\frac{15q}{8}$
$\frac{2}{5}\xf7\left(\mathrm{-10}\right)$
$-\phantom{\rule{0.2em}{0ex}}\frac{1}{25}$
$\mathrm{-18}\xf7-\left(\frac{9}{2}\right)$
In the following exercises, simplify.
$\frac{\frac{4}{5}}{\frac{8}{15}}$
$\frac{-\phantom{\rule{0.2em}{0ex}}\frac{9}{10}}{3}$
$-\phantom{\rule{0.2em}{0ex}}\frac{3}{10}$
$\frac{2}{\frac{5}{8}}$
$\frac{-\phantom{\rule{0.2em}{0ex}}\frac{x}{6}}{-\phantom{\rule{0.2em}{0ex}}\frac{8}{9}}$
Simplify Expressions Written with a Fraction Bar
In the following exercises, simplify.
$\frac{9+3}{7}$
$\frac{15}{4-9}$
$\frac{15+9}{18+12}$
$\frac{3\xb74}{\mathrm{-24}}$
$\frac{12\xb79-{3}^{2}}{3\xb718}$
$\frac{2+4\left(3\right)}{\mathrm{-3}-{2}^{2}}$
$\mathrm{-2}$
$\frac{7+3\left(5\right)}{\mathrm{-2}-{3}^{2}}$
Translate Phrases to Expressions with Fractions
In the following exercises, translate each English phrase into an algebraic expression.
the quotient of the difference of h and k , and $\mathrm{-5}$ .
Add and Subtract Fractions with a Common Denominator
In the following exercises, add.
$\frac{2}{9}+\frac{5}{9}$
$\frac{7}{p}+\frac{9}{p}$
$-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}\right)$
$-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$
$-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\right)$
In the following exercises, subtract.
$\frac{4}{5}-\phantom{\rule{0.2em}{0ex}}\frac{1}{5}$
$\frac{3}{5}$
$\frac{4}{5}-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}$
$\frac{y}{17}-\phantom{\rule{0.2em}{0ex}}\frac{9}{17}$
$\frac{y-9}{17}$
$\frac{x}{19}-\phantom{\rule{0.2em}{0ex}}\frac{8}{19}$
$-\phantom{\rule{0.2em}{0ex}}\frac{8}{d}-\phantom{\rule{0.2em}{0ex}}\frac{3}{d}$
$-\phantom{\rule{0.2em}{0ex}}\frac{11}{d}$
$-\phantom{\rule{0.2em}{0ex}}\frac{7}{c}-\phantom{\rule{0.2em}{0ex}}\frac{7}{c}$
Add or Subtract Fractions with Different Denominators
In the following exercises, add or subtract.
$\frac{1}{4}+\frac{1}{5}$
$\frac{1}{5}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{10}\right)$
$\frac{3}{10}$
$\frac{1}{2}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}\right)$
$\frac{3}{4}+\frac{2}{5}$
$\frac{11}{12}-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}$
$\frac{13}{24}$
$\frac{5}{8}-\phantom{\rule{0.2em}{0ex}}\frac{7}{12}$
$-\phantom{\rule{0.2em}{0ex}}\frac{9}{16}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}\right)$
$\frac{19}{80}$
$-\phantom{\rule{0.2em}{0ex}}\frac{7}{20}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\right)$
$1-\phantom{\rule{0.2em}{0ex}}\frac{5}{9}$
Use the Order of Operations to Simplify Complex Fractions
In the following exercises, simplify.
$\frac{{\left(\frac{1}{5}\right)}^{2}}{2+{3}^{2}}$
$\frac{1}{275}$
$\frac{{\left(\frac{1}{3}\right)}^{2}}{5+{2}^{2}}$
$\frac{\frac{2}{3}+\frac{1}{2}}{\frac{3}{4}-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}}$
14
$\frac{\frac{3}{4}+\frac{1}{2}}{\frac{5}{6}-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}}$
Evaluate Variable Expressions with Fractions
In the following exercises, evaluate.
$x+\frac{1}{2}$ when
ⓐ
$x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}$
ⓑ
$x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$
ⓐ $\frac{3}{8}$ ⓑ 0
$x+\frac{2}{3}$ when
ⓐ
$x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$
ⓑ
$x=-\phantom{\rule{0.2em}{0ex}}\frac{5}{3}$
$4{p}^{2}q$ when $p=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ and $q=\frac{5}{9}$
$\frac{5}{9}$
$5{m}^{2}n$ when $m=-\phantom{\rule{0.2em}{0ex}}\frac{2}{5}$ and $n=\frac{1}{3}$
$\frac{u+v}{w}$ when
$u=\mathrm{-4},v=\mathrm{-8},w=2$
$\mathrm{-6}$
$\frac{m+n}{p}$ when
$m=\mathrm{-6},n=\mathrm{-2},p=4$
Name and Write Decimals
In the following exercises, write as a decimal.
Nine and seven hundredths
Nine thousandths
In the following exercises, name each decimal.
Round Decimals
In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.
Add and Subtract Decimals
In the following exercises, add or subtract.
$256.37-85.49$
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