Question

Simplify the following using distributive property;
(i). $\frac{2}{5}(\frac{1}{9}+\frac{2}{5})$ (ii). $\frac{5}{12}(\frac{25}{9}+\frac{32}{5})$ (iii). $\frac{8}{9}(\frac{11}{2}+\frac{2}{9})$

Answer 1

The distributive property state that $a\times (b+c)=(a\times b)+(a\times c)$ ......(i)
(i) Given expression $\frac{2}{5}(\frac{1}{9}+\frac{2}{5})$
Applying rule of equation(i), we get
$\frac{2}{5}(\frac{1}{9}+\frac{2}{5})=(\frac{2}{5}\times \frac{1}{9})+(\frac{2}{5}\times \frac{2}{5})$
$=\frac{2}{45}+\frac{4}{25}$
$=\frac{(2\times 5)+(4\times 9)}{225}$
$=\frac{10+36}{225}$
$\therefore \frac{2}{5}(\frac{1}{9}+\frac{2}{5})=\frac{46}{225}$

(ii) Given expression $\frac{5}{12}(\frac{25}{9}+\frac{32}{5})$
Applying the rule of equation(i), we get
$\frac{5}{12}(\frac{25}{9}+\frac{32}{5})=(\frac{5}{12}\times \frac{25}{9})+(\frac{5}{12}\times \frac{32}{5})$
$=\frac{125}{108}+\frac{160}{60}$
$=\frac{(125\times 5)+(160\times 9)}{540}$
$=\frac{625+1440}{540}$
$=\frac{2065}{540}$
$\therefore \frac{5}{12}(\frac{25}{9}+\frac{32}{5})=\frac{413}{108}$

(iii) Given expression $\frac{8}{9}(\frac{11}{2}+\frac{2}{9})=(\frac{8}{9}\times \frac{11}{2})+(\frac{8}{9}\times \frac{2}{9})$
$=\frac{88}{18}+\frac{16}{81}$
$=\frac{(88\times 9)+(16\times 2)}{162}$
$=\frac{792+32}{162}$
$=\frac{824}{162}$
$\therefore \frac{8}{9}(\frac{11}{2}+\frac{2}{9})=\frac{824}{162}$