How to find a complex fraction - SSAT Upper Level Quantitative

Card 0 of 32

Simplify, writing as a proper fraction.

$$\frac{2\tfrac{1}{4}$}{5\t$\frac{2}{5}$}$

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Remember that that fraction bar is just a division symbol. Rewrite as a division, rewrite those mixed fractions as improper fractions, then rewrite as as a multiplication by the reciprocal of the second fraction.

$\frac{2\tfrac{1}{4}$}{5\t$\frac{2}{5}$} = 2\t$\frac{1}{4}$ \div 5\t$\frac{2}{5}$ = $\frac{9}{4}$ \div $\frac{27}{5}$ = $\frac{9}{4}$ \cdot $\frac{5}{27}$ = $\frac{1}{4}$ \cdot $\frac{5}{3}$= $\frac{5}{12}$

Simplify:

$$\frac{\frac{2}{3}$ + $\frac{1}{5}$}{$\frac{4}{5}$}$

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Add the fractions in the numerator, then divide the sum by the denominator:

$$\frac{\frac{2}{3}$ + $\frac{1}{5}$}{$\frac{4}{5}$}$

$=\frac{\frac{2\cdot 5}{3\cdot 5}$ + $\frac{1\cdot 3}{5\cdot 3}$}{$\frac{4}{5}$}$

$=\frac{\frac{10}{15}$ + $\frac{3}{15}$}{$\frac{4}{5}$}$

$=\frac{\frac{10+3}{15}$ }{$\frac{4}{5}$} = $\frac{\frac{13}{15}$ }{$\frac{4}{5}$}$

$= $\frac{13}{15}$ \div $\frac{4}{5}$ = $\frac{13}{15}$ \times $\frac{5}{4}$ = $\frac{13}{3}$ \times $\frac{1}{4}$ =\frac{13}{12}$$

Simplify:

$$\frac{\frac{1}{3}$ + $\frac{3}{10}$}{$\frac{9}{10}$}$

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Simplify the sum in the numerator, then divide by the denominator:

$$\frac{\frac{1}{3}$ + $\frac{3}{10}$}{$\frac{9}{10}$}$

$=\frac{\frac{1\cdot 10}{3 \cdot 10}$ + $\frac{3 \cdot 3}{10 \cdot 3}$}{$\frac{9}{10}$}$

$=\frac{\frac{10}{30}$ + $\frac{9}{30}$}{$\frac{9}{10}$}$

$=\frac{\frac{10+9}{30}$ }{$\frac{9}{10}$} = $\frac{\frac{19}{30}$ }{$\frac{9}{10}$}$

$\frac{19}{30}$ \div $\frac{9}{10}$ = $\frac{19}{30}$\times $\frac{10}{9}$ = $\frac{19}{3}$\times $\frac{1}{9}$ = $\frac{19}{27}$

Simplify:

$$\frac{5}{1\frac{1}${4}}$

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Rewrite this as a division problem, then solve:

$$\frac{5}{1\frac{1}${4}} = 5 \div 1$\frac{1}{4}$= $\frac{5}{1}$\div $\frac{5}{4}$ = $\frac{5}{1}$\times $\frac{4}{5}$= $\frac{1}{1}$\times $\frac{4}{1}$ = 4$

Simplify:

$$\frac{1\frac{1}{3}$}{4 $\frac{4}{5}$}$

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Rewrite this as a division problem, then solve:

$\frac{1\frac{1}{3}$}{4 $\frac{4}{5}$} = 1$\frac{1}{3}$ \div 4 $\frac{4}{5}$ = $\frac{4}{3}$ \div $\frac{24}{5}$= $\frac{4}{3}$ \times $\frac{5}{24}$= $\frac{1}{3}$ \times $\frac{5}{6}$= $\frac{5}{18}$

Simplify:

$$\frac{3\frac{4}{5}$}{3$\frac{1}{2}$+2$\frac{1}{5}$}$

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$$\frac{3\frac{4}{5}$}{3$\frac{1}{2}$+2$\frac{1}{5}$}$

$=3$\frac{4}{5}$ \div \left ( 3$\frac{1}{2}$+2$\frac{1}{5}$ \right )$

$= $\frac{19}{5}$ \div \left ( $\frac{7}{2}$+ $\frac{11}{5}$ \right )$

$=\frac{19}{5}$ \div \left( $\frac{35}{10}$+ $\frac{22}{10}$ \right)$

$=\frac{19}{5}$ \div $\frac{57}{10}$$

$=\frac{19}{5}$ \times $\frac{10}{57}$$

$=\frac{1 }{1}$ \times $\frac{2}{3}$ = $\frac{2}{3}$$

Simplify:

$$\frac{3\frac{1}{2}$-2$\frac{1}{5}$}{4$\frac{3}{4}$}$

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$$\frac{3\frac{1}{2}$-2$\frac{1}{5}$}{4$\frac{3}{4}$}$

$=\left ( 3$\frac{1}{2}$-2$\frac{1}{5}$ \right )\div 4$\frac{3}{4}$}$

$= \left ( $\frac{7}{2}$- $\frac{11}{5}$ \right ) \div $\frac{19}{4}$$

$= \left ( $\frac{35}{10}$- $\frac{22}{10}$ \right ) \times $\frac{4}{19}$$

$= $\frac{13}{10}$ \times $\frac{4}{19}$$

$= $\frac{13}{5}$ \times $\frac{2}{19}$$

$= $\frac{26}{95}$$

This is not among the given responses.

Simplify:

$$\frac{3\frac{1}{2}$+2$\frac{1}{5}$}{4$\frac{3}{4}$}$

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$$\frac{3\frac{1}{2}$+2$\frac{1}{5}$}{4$\frac{3}{4}$}$

$=\left ( 3$\frac{1}{2}$+2$\frac{1}{5}$ \right )\div 4$\frac{3}{4}$}$

$= \left ( $\frac{7}{2}$+ $\frac{11}{5}$ \right ) \div $\frac{19}{4}$$

$= \left ( $\frac{35}{10}$+ $\frac{22}{10}$ \right ) \times $\frac{4}{19}$$

$= $\frac{57}{10}$ \times $\frac{4}{19}$$

$= $\frac{3}{5}$ \times $\frac{2}{1}$$

$= $\frac{6}{5}$ = 1$\frac{1}{5}$$

Simplify, writing as a proper fraction.

$$\frac{2\tfrac{1}{4}$}{5\t$\frac{2}{5}$}$

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Remember that that fraction bar is just a division symbol. Rewrite as a division, rewrite those mixed fractions as improper fractions, then rewrite as as a multiplication by the reciprocal of the second fraction.

$\frac{2\tfrac{1}{4}$}{5\t$\frac{2}{5}$} = 2\t$\frac{1}{4}$ \div 5\t$\frac{2}{5}$ = $\frac{9}{4}$ \div $\frac{27}{5}$ = $\frac{9}{4}$ \cdot $\frac{5}{27}$ = $\frac{1}{4}$ \cdot $\frac{5}{3}$= $\frac{5}{12}$

Simplify:

$$\frac{\frac{2}{3}$ + $\frac{1}{5}$}{$\frac{4}{5}$}$

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Add the fractions in the numerator, then divide the sum by the denominator:

$$\frac{\frac{2}{3}$ + $\frac{1}{5}$}{$\frac{4}{5}$}$

$=\frac{\frac{2\cdot 5}{3\cdot 5}$ + $\frac{1\cdot 3}{5\cdot 3}$}{$\frac{4}{5}$}$

$=\frac{\frac{10}{15}$ + $\frac{3}{15}$}{$\frac{4}{5}$}$

$=\frac{\frac{10+3}{15}$ }{$\frac{4}{5}$} = $\frac{\frac{13}{15}$ }{$\frac{4}{5}$}$

$= $\frac{13}{15}$ \div $\frac{4}{5}$ = $\frac{13}{15}$ \times $\frac{5}{4}$ = $\frac{13}{3}$ \times $\frac{1}{4}$ =\frac{13}{12}$$

Simplify:

$$\frac{\frac{1}{3}$ + $\frac{3}{10}$}{$\frac{9}{10}$}$

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Simplify the sum in the numerator, then divide by the denominator:

$$\frac{\frac{1}{3}$ + $\frac{3}{10}$}{$\frac{9}{10}$}$

$=\frac{\frac{1\cdot 10}{3 \cdot 10}$ + $\frac{3 \cdot 3}{10 \cdot 3}$}{$\frac{9}{10}$}$

$=\frac{\frac{10}{30}$ + $\frac{9}{30}$}{$\frac{9}{10}$}$

$=\frac{\frac{10+9}{30}$ }{$\frac{9}{10}$} = $\frac{\frac{19}{30}$ }{$\frac{9}{10}$}$

$\frac{19}{30}$ \div $\frac{9}{10}$ = $\frac{19}{30}$\times $\frac{10}{9}$ = $\frac{19}{3}$\times $\frac{1}{9}$ = $\frac{19}{27}$

Simplify:

$$\frac{5}{1\frac{1}${4}}$

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Rewrite this as a division problem, then solve:

$$\frac{5}{1\frac{1}${4}} = 5 \div 1$\frac{1}{4}$= $\frac{5}{1}$\div $\frac{5}{4}$ = $\frac{5}{1}$\times $\frac{4}{5}$= $\frac{1}{1}$\times $\frac{4}{1}$ = 4$

Simplify:

$$\frac{1\frac{1}{3}$}{4 $\frac{4}{5}$}$

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Rewrite this as a division problem, then solve:

$\frac{1\frac{1}{3}$}{4 $\frac{4}{5}$} = 1$\frac{1}{3}$ \div 4 $\frac{4}{5}$ = $\frac{4}{3}$ \div $\frac{24}{5}$= $\frac{4}{3}$ \times $\frac{5}{24}$= $\frac{1}{3}$ \times $\frac{5}{6}$= $\frac{5}{18}$

Simplify:

$$\frac{3\frac{4}{5}$}{3$\frac{1}{2}$+2$\frac{1}{5}$}$

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$$\frac{3\frac{4}{5}$}{3$\frac{1}{2}$+2$\frac{1}{5}$}$

$=3$\frac{4}{5}$ \div \left ( 3$\frac{1}{2}$+2$\frac{1}{5}$ \right )$

$= $\frac{19}{5}$ \div \left ( $\frac{7}{2}$+ $\frac{11}{5}$ \right )$

$=\frac{19}{5}$ \div \left( $\frac{35}{10}$+ $\frac{22}{10}$ \right)$

$=\frac{19}{5}$ \div $\frac{57}{10}$$

$=\frac{19}{5}$ \times $\frac{10}{57}$$

$=\frac{1 }{1}$ \times $\frac{2}{3}$ = $\frac{2}{3}$$

Simplify:

$$\frac{3\frac{1}{2}$-2$\frac{1}{5}$}{4$\frac{3}{4}$}$

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$$\frac{3\frac{1}{2}$-2$\frac{1}{5}$}{4$\frac{3}{4}$}$

$=\left ( 3$\frac{1}{2}$-2$\frac{1}{5}$ \right )\div 4$\frac{3}{4}$}$

$= \left ( $\frac{7}{2}$- $\frac{11}{5}$ \right ) \div $\frac{19}{4}$$

$= \left ( $\frac{35}{10}$- $\frac{22}{10}$ \right ) \times $\frac{4}{19}$$

$= $\frac{13}{10}$ \times $\frac{4}{19}$$

$= $\frac{13}{5}$ \times $\frac{2}{19}$$

$= $\frac{26}{95}$$

This is not among the given responses.

Simplify:

$$\frac{3\frac{1}{2}$+2$\frac{1}{5}$}{4$\frac{3}{4}$}$

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$$\frac{3\frac{1}{2}$+2$\frac{1}{5}$}{4$\frac{3}{4}$}$

$=\left ( 3$\frac{1}{2}$+2$\frac{1}{5}$ \right )\div 4$\frac{3}{4}$}$

$= \left ( $\frac{7}{2}$+ $\frac{11}{5}$ \right ) \div $\frac{19}{4}$$

$= \left ( $\frac{35}{10}$+ $\frac{22}{10}$ \right ) \times $\frac{4}{19}$$

$= $\frac{57}{10}$ \times $\frac{4}{19}$$

$= $\frac{3}{5}$ \times $\frac{2}{1}$$

$= $\frac{6}{5}$ = 1$\frac{1}{5}$$

Simplify, writing as a proper fraction.

$$\frac{2\tfrac{1}{4}$}{5\t$\frac{2}{5}$}$

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Remember that that fraction bar is just a division symbol. Rewrite as a division, rewrite those mixed fractions as improper fractions, then rewrite as as a multiplication by the reciprocal of the second fraction.

$\frac{2\tfrac{1}{4}$}{5\t$\frac{2}{5}$} = 2\t$\frac{1}{4}$ \div 5\t$\frac{2}{5}$ = $\frac{9}{4}$ \div $\frac{27}{5}$ = $\frac{9}{4}$ \cdot $\frac{5}{27}$ = $\frac{1}{4}$ \cdot $\frac{5}{3}$= $\frac{5}{12}$

Simplify:

$$\frac{\frac{2}{3}$ + $\frac{1}{5}$}{$\frac{4}{5}$}$

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Add the fractions in the numerator, then divide the sum by the denominator:

$$\frac{\frac{2}{3}$ + $\frac{1}{5}$}{$\frac{4}{5}$}$

$=\frac{\frac{2\cdot 5}{3\cdot 5}$ + $\frac{1\cdot 3}{5\cdot 3}$}{$\frac{4}{5}$}$

$=\frac{\frac{10}{15}$ + $\frac{3}{15}$}{$\frac{4}{5}$}$

$=\frac{\frac{10+3}{15}$ }{$\frac{4}{5}$} = $\frac{\frac{13}{15}$ }{$\frac{4}{5}$}$

$= $\frac{13}{15}$ \div $\frac{4}{5}$ = $\frac{13}{15}$ \times $\frac{5}{4}$ = $\frac{13}{3}$ \times $\frac{1}{4}$ =\frac{13}{12}$$

Simplify:

$$\frac{\frac{1}{3}$ + $\frac{3}{10}$}{$\frac{9}{10}$}$

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Simplify the sum in the numerator, then divide by the denominator:

$$\frac{\frac{1}{3}$ + $\frac{3}{10}$}{$\frac{9}{10}$}$

$=\frac{\frac{1\cdot 10}{3 \cdot 10}$ + $\frac{3 \cdot 3}{10 \cdot 3}$}{$\frac{9}{10}$}$

$=\frac{\frac{10}{30}$ + $\frac{9}{30}$}{$\frac{9}{10}$}$

$=\frac{\frac{10+9}{30}$ }{$\frac{9}{10}$} = $\frac{\frac{19}{30}$ }{$\frac{9}{10}$}$

$\frac{19}{30}$ \div $\frac{9}{10}$ = $\frac{19}{30}$\times $\frac{10}{9}$ = $\frac{19}{3}$\times $\frac{1}{9}$ = $\frac{19}{27}$

Simplify:

$$\frac{5}{1\frac{1}${4}}$

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Rewrite this as a division problem, then solve:

$$\frac{5}{1\frac{1}${4}} = 5 \div 1$\frac{1}{4}$= $\frac{5}{1}$\div $\frac{5}{4}$ = $\frac{5}{1}$\times $\frac{4}{5}$= $\frac{1}{1}$\times $\frac{4}{1}$ = 4$