Question

Simplify;{4/3-(3/2)}+{-5/3÷30/12}+{-5/3×-27/16} step by step long answer​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

$= > (\frac{4}{3} - \frac{3}{2} ) + ( - \frac{5}{3} \div \frac{30}{12} ) + ( - \frac{5}{3} \times - \frac{27}{16} )$

✷L.C.M of 3 and 2 is 6; of 12 and 3 is 12 and of 3 and 16 is 48.

Concept :

• Product of any two value having negative sign then negative sign gets cancelled.
• Product of positive value with negative value then the resultant would be negative.

$= > ( \frac{4 \times 2 - 3 \times 3}{6} ) + (\frac{ - 5}{3} \times \frac{12}{30} ) + ( \frac{135}{48} )$

$= > ( \frac{8 - 9}{6} ) + ( \frac{\cancel{{ - 5}}}{\cancel{{3}}} \times \frac{\cancel{{12}}}{\cancel{{30}}} ) + ( - \frac{ 5}{3} \times - \frac{27}{16} )$

✷Here,12 and 30 is being cancelled by 3 and 5 respectively.

$= > - \frac{1}{6} + ( \frac{ - 1}{1} \times \frac{4}{6} ) + ( \frac{135}{48} )$

$= > - \frac{1}{6} - \frac{4}{6} + \frac{135}{48}$

✷L.C.M of 6 ,6 and 48 is 48.

$= > \frac{ - 1 \times 8 - 4 \times 8 + 135}{48}$

$= > \frac{ - 8 - 32 + 135}{48}$

$= > \frac{ - 40 + 135}{48}$

$\bold{= > \frac{95}{48} }$

Answer 2

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Explanation:

$= > (\frac{4}{3} - \frac{3}{2} ) + ( - \frac{5}{3} \div \frac{30}{12} ) + ( - \frac{5}{3} \times - \frac{27}{16} )$

✷L.C.M of 3 and 2 is 6; of 12 and 3 is 12 and of 3 and 16 is 48.

Concept :

Product of any two value having negative sign then negative sign gets cancelled.

Product of positive value with negative value then the resultant would be negative.

$= > ( \frac{4 \times 2 - 3 \times 3}{6} ) + (\frac{ - 5}{3} \times \frac{12}{30} ) + ( \frac{135}{48} )$

$= > ( \frac{8 - 9}{6} ) + ( \frac{\cancel{{ - 5}}}{\cancel{{3}}} \times \frac{\cancel{{12}}}{\cancel{{30}}} ) + ( - \frac{ 5}{3} \times - \frac{27}{16} )$

✷Here,12 and 30 is being cancelled by 3 and 5 respectively.

$= > - \frac{1}{6} + ( \frac{ - 1}{1} \times \frac{4}{6} ) + ( \frac{135}{48} )$

$= > - \frac{1}{6} - \frac{4}{6} + \frac{135}{48}$

✷L.C.M of 6 ,6 and 48 is 48.

$= > \frac{ - 1 \times 8 - 4 \times 8 + 135}{48}$

$= > \frac{ - 8 - 32 + 135}{48}$

$= > \frac{ - 40 + 135}{48}$

$\bold{= > \frac{95}{48} }$