Tag: multiplication of a fraction

Questions Related to multiplication of a fraction

Which of the following is the reciprocal of $\dfrac{7}{9}$ ?

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\dfrac {3}{7}$

  2. $\dfrac {5}{8}$

  3. $\dfrac {9}{7}$

  4. $\dfrac {6}{5}$

Show answer
Correct Option: C
Explanation:

Let $\dfrac{p}{q}=\dfrac{7}{9}$


where $p=7,q=5$

$\therefore$ the reciprocal of the given fraction $\dfrac{q}{p}=\dfrac{9}{7}$

By what number should we multiply ${(-8)}^{-1}$ to obtain ${12}^{-1}$?

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\dfrac{1}{4}$

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

  3. $-2$

  4. $\dfrac{-3}{2}$

Show answer
Correct Option: B
Explanation:

Let the number be $n$

then, 
        ${\left( { - 8} \right)^{ - 1}} \times x = {\left( {12} \right)^{ - 1}}$

        $= \dfrac{{ - 1}}{8} \times x = \dfrac{1}{{12}}$    $\because \left[ {{{\left( {\dfrac{a}{b}} \right)}^{ - n}} = {{\left( {\dfrac{b}{a}} \right)}^n}} \right]$

       $ = x = \dfrac{1}{{12}} \times  - 8$ 

       $ = x = \dfrac{{ - 2}}{3}$

Simplify $\dfrac{2}{4} \times \dfrac{3}{7}$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\dfrac{3}{14}$

  2. $\dfrac{6}{14}$

  3. $\dfrac{3}{17}$

  4. $\dfrac{6}{17}$

Show answer
Correct Option: A
Explanation:

$\cfrac{2}{4} \times \cfrac{3}{7} = \cfrac{1}{2} \times \cfrac{3}{7} = \cfrac{3}{14}$

Hence, $\cfrac{3}{14}$ is the correct answer.

A farmer has 192 animals, out of which $\dfrac{7}{16}$ are cattles. $\dfrac{2}{3}$ of cattles are dairy cows. How many dairy cows he has?

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $128$

  2. $84$

  3. $56$

  4. $112$

Show answer
Correct Option: C
Explanation:

Total number of Animals $=192$


Total number of Cattles $=\dfrac{7}{16}\times$ No. Of Animals $=\dfrac{7}{16}\times 192 = 84$

Total number of Dairy Cows $=\dfrac{2}{3}\times$ No. Of Battles $=\dfrac{2}{3}\times 84 = 56$

$\therefore$  The farmer has $56$  dairy cows

Solve: $2 \dfrac { 1 } { 2 } \mathrm {  } \text { of } 10 \mathrm { cm }$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. 30 cm

  2. 25 cm

  3. 20 cm

  4. 50 cm

Show answer
Correct Option: B
Explanation:

Given $2 \dfrac { 1 } { 2 } \mathrm {  } \text { of } 10 \mathrm { cm }$


$=2\dfrac{1}{2}\times 10$

$=\dfrac{2\cdot2+1}{2}\times 10$

$=\dfrac{5}{2}\times 10$

$=5\times 5=25$

Simplify the expression $2\dfrac{1}{4}\times \dfrac{5}{12}+\dfrac{1}{2}$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\dfrac{23}{16}$

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

  3. $4\dfrac{3}{3}$

  4. $3\dfrac{1}{5}$

Show answer
Correct Option: A
Explanation:

$2\cfrac { 1 }{ 4 } \times \cfrac { 5 }{ 12 } +\cfrac { 1 }{ 2 } $


$=\cfrac { 9 }{ 4 } \times \cfrac { 5 }{ 12 } +\cfrac { 1 }{ 2 } $

$ =\cfrac { 15 }{ 16 } +\cfrac { 1 }{ 2 } $

$ =\cfrac { 15+8 }{ 16 } $

$ =\cfrac { 23 }{ 16 } $

Reciprocal of $2\dfrac{1}{5}+3\dfrac{2}{5}$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\dfrac{11}{17}$

  2. $\dfrac{5}{28}$

  3. $\dfrac{17}{12}$

  4. $\dfrac{12}{28}$

Show answer
Correct Option: B
Explanation:
Given,

$2\dfrac{1}{5}+3\dfrac{2}{5}$

$=\dfrac{11}{5}+\dfrac{17}{5}$

$=\dfrac{28}{5}$

reciprocal is,

$=\dfrac{5}{28}$

The value of  $\displaystyle 999\frac{995}{999}\times 999$ is

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $990809$

  2. $998996$

  3. $999824$

  4. $998999$

Show answer
Correct Option: B
Explanation:

$999\dfrac { 995 }{ 999 } \times 999=\quad 999\times 995\=\dfrac { 999\times 999+995 }{ 999 } \times 999\=998996$

So correct answer will be option B

What is the value of $\cfrac{1}{9}$ of $\cfrac{1}{6}$ of $\cfrac{1}{3}$ of  $56052 ?$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $356$

  2. $336$

  3. $376$

  4. $346$

Show answer
Correct Option: D
Explanation:

Given expression $\displaystyle \frac{1}{9}\times\frac{1}{6}\times\frac{1}{3}\times56052=346$

What is the product $\displaystyle \left ( 1-\frac{1}{2} \right )\left ( 1-\frac{1}{3} \right )\left ( 1-\frac{1}{4} \right )......\left ( 1-\frac{1}{n} \right )$ equal to  when simplified?

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

  1. $\displaystyle \frac{1}{n}$

  2. $1$

  3. $2$

  4. $0$

Show answer
Correct Option: A
Explanation:

$\displaystyle \left ( 1-\frac{1}{2} \right )\left ( 1-\frac{1}{3} \right )\left ( 1-\frac{1}{4} \right )......\left ( 1-\frac{1}{n} \right )=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times ......\times \frac{n-2}{n-1}\times \frac{n-1}{n}=\frac{1}{n}$