Simplify the following using suitable properties:$\frac{3}{4} \times (4 \times \frac{7}{8})+ \frac{1}{2} \times ( 2 \times \frac{5}{7})$.

Given :

The given expression is $\frac{3}{4} \times (4 \times \frac{7}{8})+ \frac{1}{2} \times ( 2 \times \frac{5}{7})$.

To do :

We have to simplify the given expression using a suitable property.

Solution :

$\frac{3}{4} \times (4 \times \frac{7}{8})+ \frac{1}{2} \times ( 2 \times \frac{5}{7})$

The given expression can be simplified by using associative property.

$a \times (b \times c) = (a \times b) \times c $

So, the given expression can be written as,

$(\frac{3}{4} \times 4) \times \frac{7}{8} + (\frac{1}{2} \times 2) \times \frac{5}{7}$

$ = 3 \times  \frac{7}{8} + 1 \times \frac{5}{7}$

$ =\frac{21}{8} + \frac{5}{7}$

LCM of 7 and 8 is 56.

$ = \frac{21 \times 7}{8 \times 7} + \frac{5 \times 8}{7 \times 8}$

$ = \frac{147}{56} + \frac{40}{56}$

$= \frac{147+40}{56} = \frac{187}{56}$

Therefore, the value of the given expression is $\frac{187}{56}$.