Show that: 1/2 + 3/4 × 8/3 = 1/2 × 8/3 + 3/4 × 8/3 Class 9

Show that: 1/2 + 3/4 × 8/3 = 1/2 × 8/3 + 3/4 × 8/3 Class 9

Question 1.

Show that: $\left(\frac{1}{2}+\frac{3}{4}\right) \times \frac{8}{3}=\frac{1}{2} \times \frac{8}{3}+\frac{3}{4} \times \frac{8}{3}$ Class 9

Solution:

L.H.S

$\begin{aligned} & =\left(\frac{1}{2}+\frac{3}{4}\right) \times \frac{8}{3} \\ & =\left(\frac{1 \times 2}{2 \times 2}+\frac{3}{4}\right) \times \frac{8}{3} \ldots[\text { L.C.M. of } 2 \text { and } 4 \text { is } 4] \\ & =\left(\frac{2}{4}+\frac{3}{4}\right) \times \frac{8}{3} \\ & =\left(\frac{2+3}{4}\right) \times \frac{8}{3} \\ & =\frac{5}{4} \times \frac{8}{3} \\ & =\frac{5 \times 8}{4 \times 3} \\ & =\frac{40}{12}=\frac{10}{3}\end{aligned}$

R.H.S

$\begin{aligned} & =\frac{1}{2} \times \frac{8}{3}+\frac{3}{4} \times \frac{8}{3} \\ & =\frac{1 \times 8}{2 \times 3}+\frac{3 \times 8}{4 \times 3} \\ & =\frac{8}{6}+\frac{24}{12}\end{aligned}$

$\begin{array}{ll} & =\frac{8}{6}+\frac{12}{6} \\ & =\frac{8+12}{6} \\ & =\frac{20}{6}=\frac{10}{3} \\ \therefore \quad & \text { L.H.S. }=\text { R.H.S. } \\ \therefore \quad & \left(\frac{1}{2}+\frac{3}{4}\right) \times \frac{8}{3}=\frac{1}{2} \times \frac{8}{3}+\frac{3}{4} \times \frac{8}{3}\end{array}$

Question 2.

Simplify the following using the distributive property: $\frac{7}{9}\left(\frac{6}{7}-\frac{3}{4}\right)$. Class 9

Solution:

$\begin{aligned} & \frac{7}{9}\left(\frac{6}{7}-\frac{3}{4}\right) \\ & =\frac{7}{9} \times \frac{6}{7}-\frac{7}{9} \times \frac{3}{4} \quad \ldots[\text { Distributive Property] } \\ & =\frac{7 \times 6}{9 \times 7}-\frac{7 \times 3}{9 \times 4} \\ & =\frac{6}{9}-\frac{21}{36} \\ & =\frac{2}{3}-\frac{7}{12}\end{aligned}$

$\begin{aligned} & =\frac{2 \times 4}{3 \times 4}-\frac{7}{12} \quad \ldots[\text { L.C.M. of } 3 \text { and } 12 \text { is } 12 \text { ] } \\ & =\frac{8}{12}-\frac{7}{12} \\ & =\frac{8-7}{12} \\ & =\frac{1}{12} \\ \therefore \quad & \frac{7}{9}\left(\frac{6}{7}-\frac{3}{4}\right)=\frac{1}{12}\end{aligned}$