Tag: dividing fractions

Questions Related to dividing fractions

Simplify the following:
$\dfrac {3}{8} \div \dfrac {24}{48} =\dfrac{3}{4}$

maths part number dividing fractions division of a fractions division of a fraction

  1. True

  2. False

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Correct Option: A
Explanation:
$\dfrac{3}{8} \div \dfrac{{24}}{{48}} = \dfrac{3}{8} \times \dfrac{{48}}{{24}} = \dfrac{3}{4}$
Hence, the simplification is true.

Divide the sum of $\displaystyle\frac{65}{12}$ and $\displaystyle\frac{12}{7}$ by their difference.

maths part number dividing fractions division of a fractions division of a fraction

  1. $\displaystyle\frac{599}{311}$

  2. $\displaystyle\frac{680}{216}$

  3. $\displaystyle\frac{642}{133}$

  4. $\displaystyle\frac{501}{301}$

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Correct Option: A
Explanation:

sum of $\dfrac{65}{12}$  and $\dfrac{12}{7} $


$ \dfrac{65}{12} +\dfrac {12}{7}= \dfrac{65\times 7 +12\times 12}{12\times 7} $

                  $=\dfrac{599}{84}$ ......................(1)

difference of  $\dfrac{65}{12}$  and $\dfrac{12}{7} $

$\dfrac{65}{12}-\dfrac{12}{7} = \dfrac{65\times 7 - 12\times 12}{84}= \dfrac{311}{84} $

                  $ =\dfrac{311}{84} $.........................(2)

divide the sum with difference i.e.

dividing equation (1) with equation (2)

$=\dfrac{\dfrac{599}{84}}{\dfrac{311}{84}}$

$=\dfrac{599}{311}$

Divide $\dfrac{15}{38}$ by $\dfrac{-3}{19}$

maths part number dividing fractions division of a fractions division of a fraction

  1. $\dfrac{-2}{5}$

  2. $\dfrac{-5}{2}$

  3. $\dfrac{2}{5}$

  4. $\dfrac{5}{2}$

Show answer
Correct Option: B
Explanation:
$\dfrac{15}{38} \div \dfrac{-3}{19}$

$=\dfrac{15\times19}{38 \times -3}$

$=\dfrac{-5}{2}$

$\left(\large{\frac{-5}{3}}\right)^5$ $\div$ $\left(\large{\frac{-5}{3}}\right)^{7}$

maths part number dividing fractions division of a fractions division of a fraction

  1. $\large{\frac{25}{9}}$

  2. $\large{\frac{9}{25}}$

  3. $\large{\frac{16}{25}}$

  4. $\large{\frac{25}{16}}$

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Correct Option: B
Explanation:

$\left(\large{\frac{-5}{3}}\right)^5$ $\div$ $\left(\large{\frac{-5}{3}}\right)^{7}$


$=-\left(\large{\frac{5}{3}}\right)^5$ $\times$ $-\left(\large{\frac{3}{5}}\right)^{7}$


$=\left(\dfrac{3}{5}\right)^2$

$=\dfrac{9}{25}$.

Evaluate: $\dfrac {\left(\dfrac {-3}{5}\right)^{3} \times \left(\dfrac {9}{25}\right)^{2} \times \left(\dfrac {-18}{125}\right)^{o}}{\left(\dfrac {-27}{125}\right) \times \left(\dfrac {-3}{5}\right)}$

maths part number dividing fractions division of a fractions division of a fraction

  1. $\dfrac{27}{125}$

  2. $-\dfrac{27}{125}$

  3. $\dfrac{64}{125}$

  4. $-\dfrac{64}{125}$

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Correct Option: B
Explanation:

$\dfrac {\left(\dfrac {-3}{5}\right)^{3} \times \left(\dfrac {9}{25}\right)^{2} \times \left(\dfrac {-18}{125}\right)^{0}}{\left(\dfrac {-27}{125}\right) \times \left(\dfrac {-3}{5}\right)}=\dfrac{\dfrac{-3^3\times 3^4\times 1}{5^3\times 5^4\times 1}}{\dfrac{3^3\times 3}{5^3\times 5}}=-\dfrac{3^{7-4}}{5^{7-4}}=-\dfrac{27}{125}$

Convert the following into fraction.
$22.5\%$

maths part number dividing fractions division of a fractions division of a fraction
    • $\dfrac{9}{40}$

  2. $\dfrac{225}{100}$

  3. $\dfrac{22}{100}$

  4. $\dfrac{5}{100}$

Show answer
Correct Option: A
Explanation:
     $22.5$%
$=\dfrac{22.5}{100}$
$=\dfrac{48}{2}\times \dfrac{1}{100}$
$=\dfrac{9}{40}$

Evaluate the following :

$\displaystyle  8 \times \dfrac {\dfrac{5}{24}}{\dfrac {7}{12}} $.

maths part number dividing fractions division of a fractions division of a fraction

  1. $\displaystyle \frac {5 }{24}$

  2. $\displaystyle \frac {20}{7}$

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

  4. $\displaystyle \frac {21}{5}$

Show answer
Correct Option: B
Explanation:

Given, $ 8 \times \displaystyle \frac {\frac {5}{24}}{\frac {7}{12}} $

$ \therefore 8 \times \displaystyle \frac {\frac {5 }{24}}{\frac {7}{12}} = 8 \times \frac {5\times 12}{7 \times 24}   $

$=\displaystyle \frac {5 \times 4}{7}$

$= \displaystyle \frac {20}{7} $

$I = \displaystyle \frac{3}{4}\div \frac{5}{6}$ 

$II = 3\displaystyle \div $[($4\displaystyle \div 5$)$\displaystyle \div 6$]
$III = [3\displaystyle \div (4\displaystyle \div 5)]\displaystyle \div 6$
$IV = 3\displaystyle \div 4(5\displaystyle \div 6)$
Select the correct option from the following.

maths part number dividing fractions division of a fractions division of a fraction

  1. I and II are equal

  2. I and IV are equal

  3. I and III are equal

  4. All are equal

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Correct Option: B
Explanation:

$ I=\cfrac{3}{4}\times \cfrac{6}{5}=\cfrac{9}{10}$


$II=3\div \left [ \cfrac{4}{5}\times \cfrac{1}{6} \right ]=3\times \cfrac{15}{2}=\cfrac{45}{2}$
$III=\left [ 3\div \cfrac{4}{5} \right ]\div 6=3\times \cfrac{5}{4}\times \cfrac{1}{6}=\cfrac{5}{8}$
$ IV=3\div 4\times\cfrac{5}{6}=3\times \cfrac{3}{10}=\cfrac{9}{10}$

Hence, $I$ and $IV$ are equal.

The least fraction that must be added to $\displaystyle1\frac{1}{3}\div 1\frac{1}{2}\div 1\frac{1}{9}$  to make the result an integer is:

maths part number dividing fractions division of a fractions division of a fraction

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

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

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

  4. $\displaystyle\frac{1}{5}$

Show answer
Correct Option: D
Explanation:

$\displaystyle 1\frac{1}{3}\div 1\frac{1}{2}=\frac{4}{3}\div \frac{3}{2}\div \frac{10}{9}$
$\displaystyle =\frac{4}{3}\times \frac{2}{3}\div \frac{10}{9}=\frac{8}{9}\times \frac{9}{10}=\frac{4}{5}$
$\displaystyle \therefore \frac{1}{5}$ should be added to $\displaystyle \frac{4}{5}$ to make it an integer

The number of positive fractions m/n such that $1/3< m/n < 1$ and having the property that the fraction remains the same by adding some positive integer to the numerator and multiplying the denominator by the same positive integer is

maths part number dividing fractions division of a fractions division of a fraction

  1. $1$

  2. $3$

  3. $6$

  4. infinite

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Correct Option: B
Explanation:

$m, n$ are integer
$1/3 < m/n < 1 $...(i)
$\displaystyle \frac{m + \alpha}{n \alpha} = \frac{m}{n}        n \neq 0$
$\alpha = \displaystyle \frac{m}{m - 1} = +$ve integer
$\therefore m = 2$
Using equation (i)
$n = 3, 4, 5$
$\therefore \displaystyle \frac{m}{n}= \frac{2}{3} , \frac{2}{4}, \frac{2}{5}$