Tag: simplest ratio

$ 5m-n=m+2n \$
$ => 4m = 3n \$
$ => \dfrac {m}{n} = \dfrac {3}{4} \$
$ => m : n = 3:4 $

Let $ m = 3a ; n = 4a $

Given, $ 2a-5b = 0 $
$=>. 2a = 5b $
$ => \frac {a}{b} = \frac {5}{2} $
 
Now, $ \frac {a+b}{b} = \frac {a}{b} + 1 = \frac {5}{2} + 1 = \frac{5+2}{2} = \frac {7}{2} $

In the given ratios "b" is

the common term, and the values of b in both ratios are not equal.

To make them equal, find the L.C.M.

of values corresponding to b i.e., $ 8 $ and $ 12 $.





L.C.M. of $ 8  $ and $ 12 = 24 $





Therefore, an equivalent ratio of $ a:b $ such that $ b = 24 $ is $= 7 \times 3:8 \times 3 = 21:24 $

Similarly, an equivalent ratio of $ b:c$ is $ = 12 \times 2 :7 \times 2 = 24:14 $





Therefore,$ a: c = 21:14 $

Dividing by $ 7 $

$ a:c = 3:2 $

$\left( \sqrt { 169-144 }  \right) \div \left( \sqrt { 64+36 }  \right) \ =\sqrt { 25 } \div \sqrt { 100 } =5\div 10=\displaystyle\frac { 5 }{ 10 } =0.5$

$\displaystyle \frac {2}{5}\, =\, \displaystyle \frac {2}{5}\, \times\, \displaystyle \frac {3}{3}\, =\, \displaystyle \frac {6}{15}$

$\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {1\, \times\, 2}{2\, \times\, 2}\, =\, \displaystyle \frac {2}{4}$

$\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {3}{6}\, =\, \displaystyle \frac {5}{10}\, =\, \displaystyle \frac {9}{18}$

$\displaystyle \frac {15}{45}\, =\, \displaystyle \frac {15\, \div\, 5}{45\, \div\, 5}\, =\, \displaystyle \frac {3}{9}$

${.225}\Rightarrow \frac{225}{1000}=\frac{9}{40}$

$1.\bar{3}$
Let $1.3333...$ be $x$
$1.3333...=x$  {i}
$13.333...=10x$ {ii} [Multiplied by $10$]
                               
$        12  =9x$
$=>x=\frac{12}{9}$
$=>x=\frac{4}{3}$