Tag: maths

Questions Related to maths

State whether true or false
Simplest form of the ratio 225% in form of ratio is $\displaystyle \frac{9}{4}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Given percentage is $ 225 % $

In fraction form, $ 225  % $ $  = \dfrac {225}{100} $

Simplifying it by dividing the numerator and denominator by $ 25  $, we get the fraction $ = \dfrac {9}{4} $

If $2a-5b = 0$ then find the value of $\displaystyle \frac{a+b}{a-b}$.

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\displaystyle \frac{7}{2}$

  2. $\displaystyle \frac{7}{3}$

  3. $\displaystyle \frac{3}{2}$

  4. $\displaystyle \frac{7}{5}$

Show answer
Correct Option: B
Explanation:

Given, $ 2a-5b = 0 $

$=>2a = 5b $

$ => \dfrac {a}{b} = \dfrac {5}{2} $

Applying componendo and dividendo,

Now, $ \dfrac {a+b}{a-b} = \dfrac{5+2}{5-2} =

\dfrac {7}{3} $

If $2a-5b = 0$ then find the value of  $\displaystyle \frac{a-b}{b}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\displaystyle \frac{7}{2}$

  2. $\displaystyle \frac{3}{2}$

  3. $\displaystyle \frac{5}{2}$

  4. $\displaystyle \frac{7}{5}$

Show answer
Correct Option: B
Explanation:

Given, $ 2a-5b = 0 $
$=> 2a = 5b $
$ => \dfrac {a}{b} = \dfrac {5}{2} $
 
Now, $ \dfrac {a-b}{b} = \dfrac {a}{b} - 1 = \dfrac {5}{2} - 1 = \dfrac{5-2}{2} = \dfrac {3}{2} $

State true or false.
If $5m-n=m+2n$ then the value of $(4m + n) : (4m - n)$ is $2:1$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

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

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


So, $ (4m + n) : (4m - n) = 4(3a) + 4a : 4(3a) -4a $

$ => (4m + n) : (4m - n) = 16a:8a = 2: 1 $

If $2a-5b = 0$ then find the value of  $\displaystyle \frac{a+b}{b}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\displaystyle \frac{7}{2}$

  2. $\displaystyle \frac{7}{5}$

  3. $\displaystyle \frac{2}{7}$

  4. $\displaystyle \frac{7}{6}$

Show answer
Correct Option: A
Explanation:

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} $

If a : b = 7 : 8 and b : c = 12 : 7 then find a : c in the simplest form is 3:2

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

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 $

Find the value of $\left( \sqrt { 169-144 }  \right) \div \left( \sqrt { 64+36 }  \right) $

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. 0.5

  2. 0.25

  3. 2.5

  4. 5

Show answer
Correct Option: A
Explanation:

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

$\displaystyle \frac {2}{5}\, =\, \displaystyle \frac {?}{15}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. 2

  2. 3

  3. 5

  4. 6

Show answer
Correct Option: D
Explanation:

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

The fraction equivalent to $\displaystyle \frac {1}{2}$ is

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\displaystyle \frac {2}{4}$

  2. $\displaystyle \frac {3}{6}$

  3. $\displaystyle \frac {8}{16}$

  4. All the above

Show answer
Correct Option: D
Explanation:

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


$\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {1\, \times\, 3}{2\, \times\, 3}\, =\, \displaystyle \frac {3}{6}$

$\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {1\, \times\, 8}{2\, \times\, 8}\, =\, \displaystyle \frac {8}{16}$

So $\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {2}{4}\, =\, \displaystyle \frac {3}{6}\, =\, \displaystyle \frac {8}{16}$

The fraction equivalent to $\displaystyle \frac {1}{2}$ is .......... 

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\displaystyle \frac {3}{6}$

  2. $\displaystyle \frac {5}{10}$

  3. $\displaystyle \frac {9}{8}$

  4. All the above

Show answer
Correct Option: D
Explanation:

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