Question

Simplify and write the answer in the simplest from​

Answer 1

Answer:

Question 1

$\bigg[ \frac{1}{2} + \frac{3}{8} \bigg] \times \bigg[ \frac{7}{3} + \frac{1}{6} \bigg]$

• $\bigg[ \frac{1}{2} + \frac{3}{8} \bigg] \times \bigg[ \frac{7}{3} + \frac{1}{6} \bigg]$

• $\bigg[ \frac{4}{10} \bigg] \times \bigg[ \frac{8}{9} \bigg]$

• $\bigg[ \frac{4}{10} \bigg] \times \bigg[ \frac{8}{9} \bigg] = \frac{32}{90}$

$\cancel\frac{32}{90} = \bold{\frac{16}{45} }$

Answer 2

$\sf\huge\bold{Answer:}$

$\fbox{Solution:1}$

Given :

$\tt \bigg( \frac{1}{2} + \frac{3}{8} \bigg) \times \bigg( \frac{7}{3} + \frac{1}{6} \bigg)$

To find :

Simplest form

Solution :

$\bf \red{ \bigg( \frac{1}{2} + \frac{3}{8} \bigg) \times \bigg( \frac{7}{3} + \frac{1}{6} \bigg) }$

$\tt \bigg( \frac{8 \times 1 + 3 \times 2}{8 \times 2} \bigg) \times \bigg( \frac{7 \times 6 + 1 \times 3}{3 \times 6} \bigg)$

$= \tt \bigg( \frac{8 + 6}{16} \bigg) \times \bigg( \frac{42 + 3}{18} \bigg)$

$= \tt \bigg( \frac{14}{16} \bigg) \times \bigg( \frac{45}{18} \bigg)$

$= \tt \cancel\frac{14}{16} \times \cancel\frac{45}{18}$

$\tt \: = \frac{7}{8} \times \frac{13}{9}$

$\tt\ = \frac{91}{72}$

$\boxed{ \boxed{\tt\purple{ \frac{91}{72} }} }$

$\fbox{Solution:2}$

Given :

$\tt \bigg( - \frac{ 4}{9} + \frac{2}{3} \bigg) \times \bigg( \frac{11}{15} - \frac{2}{5} \bigg)$

To find :

Simplest form

Solution :

$\bf \red{ \bigg( - \frac{ 4}{9} + \frac{2}{3} \bigg) \times \bigg( \frac{11}{15} - \frac{2}{5} \bigg)}$

$\tt \bigg( \frac{ - 4 \times3 + 2 \times 9 }{9 \times 3} \bigg) \times \bigg( \frac{11 \times 5 - 2 \times 15}{15 \times 5} \bigg)$

$= \tt \bigg( \frac{ - 12 + 18 }{21} \bigg) \times \bigg( \frac{55 - 30}{75} \bigg)$

$= \tt \bigg( \frac{ 6 }{21} \bigg) \times \bigg( \frac{20}{75} \bigg)$

$= \tt \cancel \frac{ 6 }{21} \times \cancel\frac{20}{75}$

$\tt\ = \frac{2}{7} \times \frac{4}{15}$

$\tt = \frac{8}{85}$

$\boxed{ \boxed{\tt\purple{ \frac{8}{85} }} }$

$\fbox{Solution:3}$

Given :

$\tt \bigg( \frac{ 5}{8} - \frac{7}{16} \bigg) \times \bigg( \frac{1}{3} + \frac{11}{6} - \frac{5}{18} \bigg)$

To find :

Simplest form

Solution :

$\bf \red{\bigg( \frac{ 5}{8} - \frac{7}{16} \bigg) \times \bigg( \frac{1}{3} + \frac{11}{6} - \frac{5}{18} \bigg)}$

$= \tt \bigg( \frac{ 5 \times 2 - 7 \times 1}{16} \bigg) \times \bigg( \frac{1 \times 6 + 11 \times 3 - 5 \times 1}{18 } \bigg)$

$= \tt \bigg( \frac{ 10 - 7 }{16} \bigg) \times \bigg( \frac{ 6 + 33 - 5 }{18 } \bigg)$

$= \tt \bigg( \frac{ 3}{16} \bigg) \times \bigg( \frac{ 34}{18 } \bigg)$

$\tt = \frac{ 3}{16} \times \cancel\frac{ 34}{18 }$

$\tt = \frac{ \cancel 3}{16} \times \frac{ 17}{ \cancel 9 }$

$\tt\ = \frac{ 1}{16} \times \frac{ 17}{3 }$

$\tt\ = \frac{ 17}{48 }$

$\boxed{ \boxed{\tt\purple{ \frac{17}{48} }} }$

$\fbox{Solution:4}$

Given :

$\tt \bigg( \frac{ 2}{5} - \frac{1}{10} + \frac{7}{15} \bigg) \times \bigg( \frac{1}{2} - \frac{9}{16} + \frac{3}{8} \bigg)$

To find :

Simplest form

Solution :

$\bf \red{ \bigg( \frac{ 2}{5} - \frac{1}{10} + \frac{7}{15} \bigg) \times \bigg( \frac{1}{2} - \frac{9}{16} + \frac{3}{8} \bigg)}$

$= \tt \bigg( \frac{ 2 \times 3 - 1 \times 2 + 7 \times 1}{15} \bigg) \times \bigg( \frac{1 \times 8 - 9 \times 1 + 2 \times 3}{16} \bigg)$

$= \tt \bigg( \frac{ 6 - 2 + 7}{15} \bigg) \times \bigg( \frac{ 8 - 9 + 6}{16} \bigg)$

$= \tt \frac{ 11}{ \cancel15} \times \frac{ \cancel5}{16}$

$= \tt \frac{ 11}{ 3} \times \frac{ 1}{16}$

$= \tt \frac{ 11}{ 48}$

$\boxed{ \boxed{\tt\purple{ \frac{11}{48} }} }$