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Translate and solve. The quotient of $n$ and $\frac{2}{3}$ is $\frac{5}{12}.$
$\frac{\phantom{\rule{0.2em}{0ex}}n\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{2}{3}\phantom{\rule{0.2em}{0ex}}}=\frac{5}{12};n=\frac{5}{18}$
Translate and solve The quotient of $c$ and $\frac{3}{8}$ is $\frac{4}{9}.$
$\frac{\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{3}{8}\phantom{\rule{0.2em}{0ex}}}=\frac{4}{9};c=\frac{1}{3}$
Translate and solve: The sum of three-eighths and $x$ is three and one-half.
Translate. | |
Use the Subtraction Property of Equality to subtract $\frac{3}{8}$ from both sides. | |
Combine like terms on the left side. | |
Convert mixed number to improper fraction. | |
Convert to equivalent fractions with LCD of 8. | |
Subtract. | |
Write as a mixed number. |
We write the answer as a mixed number because the original problem used a mixed number.
Check:
Is the sum of three-eighths and $3\frac{1}{8}$ equal to three and one-half?
$\frac{3}{8}+3\frac{1}{8}\stackrel{?}{=}3\frac{1}{2}$ | |
Add. | $3\frac{4}{8}\stackrel{?}{=}3\frac{1}{2}$ |
Simplify. | $3\frac{1}{2}=3\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\u2713$ |
The solution checks.
Translate and solve: The sum of five-eighths and $x$ is one-fourth.
$\frac{5}{8}+x=\frac{1}{4};x=-\frac{3}{8}$
Translate and solve: The difference of one-and-three-fourths and $x$ is five-sixths.
$1\frac{3}{4}-x=\frac{5}{6};\phantom{\rule{0.2em}{0ex}}x=\frac{11}{12}$
Determine Whether a Fraction is a Solution of an Equation
In the following exercises, determine whether each number is a solution of the given equation.
$x-\frac{2}{5}=\frac{1}{10}\text{:}$
$y-\frac{1}{3}=\frac{5}{12}\text{:}$
$h+\frac{3}{4}=\frac{2}{5}\text{:}$
$k+\frac{2}{5}=\frac{5}{6}\text{:}$
Solve Equations with Fractions using the Addition, Subtraction, and Division Properties of Equality
In the following exercises, solve.
$y+\frac{1}{3}=\frac{4}{3}$
$f+\frac{9}{10}=\frac{2}{5}$
$a-\frac{5}{8}=-\frac{7}{8}$
$x-\left(-\frac{3}{20}\right)=-\frac{11}{20}$
$n-\frac{1}{6}=\frac{3}{4}$
$s+\left(-\frac{1}{2}\right)=-\frac{8}{9}$
$k+\left(-\frac{1}{3}\right)=-\frac{4}{5}$
$k=-\frac{7}{15}$
$\mathrm{-4}w=26$
Solve Equations with Fractions Using the Multiplication Property of Equality
In the following exercises, solve.
$\frac{f}{4}=\mathrm{-20}$
$\frac{y}{7}=\mathrm{-21}$
$\frac{p}{\mathrm{-5}}=\mathrm{-40}$
$\frac{r}{\mathrm{-12}}=\mathrm{-6}$
$-h=-\frac{5}{12}$
$\frac{4}{5}n=20$
$\frac{3}{8}q=\mathrm{-48}$
$-\frac{2}{9}a=16$
$-\frac{6}{11}u=\mathrm{-24}$
Mixed Practice
In the following exercises, solve.
$4f=\frac{4}{5}$
$p+\frac{2}{3}=\frac{1}{12}$
$\frac{7}{8}m=\frac{1}{10}$
$-\frac{2}{5}=x+\frac{3}{4}$
$\frac{11}{20}=\text{\u2212}\mathit{\text{f}}$
$\frac{8}{15}=\text{\u2212}\mathit{\text{d}}$
$d=-\frac{8}{15}$
Translate Sentences to Equations and Solve
In the following exercises, translate to an algebraic equation and solve.
$n$ divided by eight is $\mathrm{-16}.$
$n$ divided by six is $\mathrm{-24}.$
$\frac{n}{6}=\mathrm{-24};n=\mathrm{-144}$
$m$ divided by $\mathrm{-9}$ is $\mathrm{-7}.$
$m$ divided by $\mathrm{-7}$ is $\mathrm{-8}.$
$\frac{m}{\mathrm{-7}}=\mathrm{-8};m=56$
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