Question

Express the following rations in the simplest form.
$1)6:8$ $2)21:24$ $3)33:77$ $4)25:125$ $5)\frac{2}{3}:\frac{3}{5}$ $6)\frac{4}{5}:\frac{3}{8}$ $7)1\frac{1}{2}:4\frac{1}{2}$
$8)\frac{1}{3}:2$

Answer 1

We have,

$1)6:8$

$\Rightarrow \frac{6}{8}$

$\Rightarrow \frac{2\times 3}{2\times 4}$

$\Rightarrow \frac{3}{4}$

$\Rightarrow 3:4$

$2)21:24$

$\Rightarrow \frac{21}{24}$

$\Rightarrow \frac{3\times 7}{3\times 8}$

$\Rightarrow \frac{7}{8}$

$\Rightarrow 7:8$

$3)33:77$

$\Rightarrow \frac{33}{77}$

$\Rightarrow \frac{3\times 11}{7\times 11}$

$\Rightarrow \frac{3}{7}$

$\Rightarrow 3:7$

$4)25:125$

$\Rightarrow \frac{25}{125}$

$\Rightarrow \frac{1\times 25}{5\times 25}$

$\Rightarrow \frac{1}{5}$

$\Rightarrow 1:5$

$5)\frac{2}{3}:\frac{3}{5}$

$\Rightarrow \frac{\frac{2}{3}}{\frac{3}{5}}$

$\Rightarrow \frac{5\times 2}{3\times 3}$

$\Rightarrow \frac{10}{9}$

$\Rightarrow 10:9$

$6)\frac{4}{5}:\frac{3}{8}$

$\Rightarrow \frac{\frac{4}{5}}{\frac{3}{8}}$

$\Rightarrow \frac{4\times 8}{5\times 3}$

$\Rightarrow \frac{32}{15}$

$\Rightarrow 32:15$

$7)1\frac{1}{2}:4\frac{1}{2}$

$\frac{3}{2}:\frac{9}{2}$

$\Rightarrow \frac{\frac{3}{2}}{\frac{9}{2}}$

$\Rightarrow \frac{3\times 2}{9\times 2}$

$\Rightarrow \frac{1}{3}$

$\Rightarrow 1:3$

$8)\frac{1}{3}:2$

$\Rightarrow \frac{\frac{1}{3}}{2}$

$\Rightarrow \frac{1}{3\times 2}$

$\Rightarrow \frac{1}{6}$

$\Rightarrow 1:6$

Hence, this is the answer.