Prove that the following rational numbers are equal: i. 2/3 and 4/6 ii. 5/4 and 10/8 Class 9

Prove that the following rational numbers are equal: i. 2/3 and 4/6 ii. 5/4 and 10/8 Class 9

Question 1.

Prove that the following rational numbers are equal: Class 9

i. $\quad \frac{2}{3}$ and $\frac{4}{6}$

ii. $\frac{5}{4}$ and $\frac{10}{8}$

iii. $-\frac{3}{5}$ and $-\frac{6}{10}$

iv. $\frac{9}{3}$ and 3

Solution:

Two rational numbers [latex]\frac{a}{b} \text { and } \frac{c}{d}[/latex] are equal if ad = bc.

$\begin{array}{ll}\text { i. } & \frac{2}{3} \text { and } \frac{4}{6} \\ & 2 \times 6=12 \text { and } 3 \times 4=12 \\ \therefore & \frac{2}{3}=\frac{4}{6}\end{array}$

$\begin{aligned} & \text { ii. } \quad \frac{5}{4} \text { and } \frac{10}{8} \\ & 5 \times 8=40 \text { and } 4 \times 10=40 \\ & \therefore \quad \frac{5}{4}=\frac{10}{8}\end{aligned}$

$\begin{aligned} & \text { iii. } \quad \frac{-3}{5} \text { and } \frac{-6}{10} \\ & (-3) \times 10=-30 \text { and } 5 \times(-6)=-30 \\ & \therefore \quad \frac{-3}{5}=\frac{-6}{10}\end{aligned}$

$\begin{array}{ll}\text { iv. } & \frac{9}{3} \text { and } 3 \\ & \text { i.e., } \frac{9}{3} \text { and } \frac{3}{1} \\ & 9 \times 1=9 \text { and } 3 \times 3=9 \\ \therefore \quad & \frac{9}{3}=3\end{array}$