Question

Evaluate:
ii) $(\frac{8}{15}\times \frac{-25}{16})+(\frac{-18}{35}\times \frac{5}{6})$

Answer 1

Step 1: Using the concept of multiplication of rational numbers
Given, $(\frac{8}{15}\times \frac{-25}{16})+(\frac{-18}{35}\times \frac{5}{6})$

Consider $(\frac{8}{15}\times \frac{-25}{16})$$=\frac{-8\times 25}{15\times 16}=\frac{-5}{6}$

$\therefore (\frac{-18}{35}\times \frac{5}{6})$$=\frac{-18}{35}\times \frac{5}{6}=\frac{-18\times 5}{35\times 6}=-\frac{3}{7}$

Step 2: Finding the required value
Given, $(\frac{8}{15}\times \frac{-25}{16})+(\frac{-18}{35}\times \frac{5}{6})$
$=\frac{-5}{6}+\frac{-3}{7}$
$=\frac{-5\times 7}{6\times 7}+\frac{-3\times 6}{7\times 6}$

[LCM of $6,7=6\times 7=42$]

$=\frac{-35}{42}+\frac{-18}{42}$
$=\frac{-35+(-18)}{42}$
$=\frac{-53}{42}$

Hence, the required result is $\frac{-53}{42}$.