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Using distributivity, find:
$\left(\frac{8}{15}\right) \ \left(\frac{-7}{18} \ +\ \frac{-11}{18}\right)$.
Given: $\left(\frac{8}{15}\right) \ \left(\frac{-7}{18} \ +\ \frac{-11}{18}\right)$
To find: Here we have to find the value of the given expression $\left(\frac{8}{15}\right) \ \left(\frac{-7}{18} \ +\ \frac{-11}{18}\right)$ using distributive property.
Solution:
The distributive property of multiplication over addition for rational numbers is as follows:
If a, b and c, are three rational numbers, then
$a \times (b + c) = (a \times b) + (a \times c)$
So,
$\left(\frac{8}{15}\right) \ \ \left(\frac{-7}{18} \ +\ \frac{-11}{18}\right)$
$=\ \left(\frac{8}{15} \ \times \ \left(\frac{-7}{18}\right)\right) \ +\ \left(\frac{8}{15} \ \times \ \left(\frac{-11}{18}\right)\right)$
$=\ \left(\frac{4}{15} \ \times \ \left(\frac{-7}{9}\right)\right) \ +\ \left(\frac{4}{15} \ \times \ \left(\frac{-11}{9}\right)\right)$
Following BODMAS, solve the bracket first,
$=\ \left(\frac{-28}{135}\right) \ +\ \left(\frac{-44}{135}\right)$
$=\ \frac{-\ 28\ -\ 44}{135}$
$=\ -\ \frac{72}{135}$
Divide both numerator and denominators by common factor 9:
$=\mathbf{\ -\ \frac{8}{15}}$
So, the answer is $-\ \frac{8}{15}$.
Updated on: 10-Oct-2022
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