What is ((3/2 1/2-2/3)^2)/((1-2/7 sqrt(49/9))^2) ?

The solution to ((3/2 1/2-2/3)^2)/((1-2/7 sqrt(49/9))^2) is 1/16

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simplify ((3/2 1/2-2/3)^2)/((1-2/7 sqrt(49/9))^2)

simplify

\frac{( \frac{3}{2} \frac{1}{2} - \frac{2}{3} ) ^{2}}{( 1 - \frac{2}{7} \frac{49}{9} ) ^{2}}

\frac{1}{16}

Decimal Notation

0.0625

Solution steps

\frac{( \frac{3}{2} \cdot \frac{1}{2} - \frac{2}{3} ) ^{2}}{( 1 - \frac{2}{7} \frac{49}{9} ) ^{2}}

(\frac{3}{2} \cdot \frac{1}{2} - \frac{2}{3})^{2} = \frac{1}{144}

= \frac{\frac{1}{144}}{( 1 - \frac{2}{7} \frac{49}{9} ) ^{2}}

Expand

(1 - \frac{2}{7} \frac{49}{9})^{2} : \frac{1}{9}

= \frac{\frac{1}{144}}{\frac{1}{9}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{1 \cdot 9}{144 \cdot 1}

Cancel

\frac{1 \cdot 9}{144 \cdot 1} : \frac{1}{16}

= \frac{1}{16}

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What is ((3/2 1/2-2/3)^2)/((1-2/7 sqrt(49/9))^2) ?
The solution to ((3/2 1/2-2/3)^2)/((1-2/7 sqrt(49/9))^2) is 1/16