Simplify:$ 5 \frac{1}{4} \p 2 \frac{1}{3}-4 \frac{2}{3} \p 5 \frac{1}{3} \times 3 \frac{1}{2} $

Given:

\( 5 \frac{1}{4} \div 2 \frac{1}{3}-4 \frac{2}{3} \div 5 \frac{1}{3} \times 3 \frac{1}{2} \)

To do:

We have to simplify the given expression.

Solution:

$5 \frac{1}{4} \div 2 \frac{1}{3}-4 \frac{2}{3} \div 5 \frac{1}{3} \times 3 \frac{1}{2}=\frac{5\times4+1}{4}\div \frac{2\times3+1}{3}-\frac{4\times3+2}{3}\div \frac{5\times3+1}{3}\times \frac{3\times2+1}{2}$

$=\frac{21}{4}\div\frac{7}{3}-\frac{14}{3}\div \frac{16}{3}\times\frac{7}{2}$

$=\frac{21}{4}\times\frac{3}{7}-\frac{14}{3}\times\frac{3}{16}\times\frac{7}{2}$

$=\frac{3\times3}{4}-\frac{7\times7}{16}$

$=\frac{9}{4}-\frac{49}{16}$

$=\frac{9\times4-49}{16}$

$=\frac{36-49}{16}$

$=\frac{-13}{16}$

Therefore, $5 \frac{1}{4} \div 2 \frac{1}{3}-4 \frac{2}{3} \div 5 \frac{1}{3} \times 3 \frac{1}{2}=\frac{-13}{16}$. 

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Updated on: 10-Oct-2022

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