Question

the product of reciprocal of [ 5/3+7/9-3/2] and the reciprocal of [ 5/7×21/4+3/8×[-512/81] is​

Answer 1

Answer: $\frac{243}{-544}$

Step-by-step explanation:

First solve the 1st bracket

Addition

$\frac{5}{3} + \frac{7}{9} \\=\frac{15}{9} + \frac{7}{9} \\ =\frac{22}{9}$

Subtraction

$\frac{22}{9} - \frac{3}{2}$

$\frac{44-27}{18} \\=\frac{17}{18}$

Next solve the 2nd bracket

$\frac{5}{7}$ x $\frac{21}{4}$ + $\frac{3}{8}$ x $\frac{-512}{81}$

According to BODMAS, first multiplication

$\frac{5}{7}$ x $\frac{21}{4}$ = $\frac{105}{28}$

$\frac{3}{8}$ x $\frac{-512}{81}$ (If you can simplify the values first you have to simplify. Numerators-Denominators)

3 and 81 can be simplified by 3 (81/3=27)

8 and 512 can be simplified by 8 (512/8 = 64)

So,

=$\frac{-64}{27}$

Now you have to multiply the reciprocal of both answers.

Reciprocal of 17/18 is 18/17

Reciprocal of 64/27 is 27/-64

$\frac{18}{17}$ x $\frac{27}{-64}$

Multiply numerator with numerator and denominator with denominator.

$\frac{486}{-1088}$

This can be simplified by 2

$\frac{243}{-544}$