Tag: multiplication of a fraction

Questions Related to multiplication of a fraction

Multiply and reduce to lowest form:
$\cfrac { 2 }{ 3 } \times 5\cfrac { 1 }{ 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. $3\cfrac { 7 }{ 15 } $

  2. $7\cfrac { 3 }{ 15 } $

  3. $\cfrac { 7 }{ 15 } $

  4. $3\cfrac { 3 }{ 15 } $

Show answer
Correct Option: A
Explanation:

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


Can be written as


$\dfrac{2}{3}\times \dfrac{26}{5}$

$=\dfrac{52}{15}$

$=3\dfrac{7}{15}$

Deepak can paint $\cfrac { 2 }{ 5 } $ of a house in one day. If he continuous working at this rate, how many days will he take to paint the whole house?

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

  1. $2\cfrac { 1 }{ 2 } $ days

  2. $1\cfrac { 1 }{ 2 } $ days

  3. $\cfrac { 1 }{ 2 } $ days

  4. $2\cfrac { 1 }{ 4 } $ days

Show answer
Correct Option: A
Explanation:

$\boxed{\text{Work(W)}\propto \text{Days(D)}\\dfrac{W _1}{D _1}=\dfrac{W _2}{D _2}}$

given,
$W _1=\dfrac25\quad D _1=1\,\text{day}\W _2=1\,\,\text{(painting the whole house)}$
to find, $D _2=?$

$\dfrac{2/5}{1}=\dfrac{1}{D _2}\Rightarrow D _2=\dfrac52$

$\therefore D _2=2\dfrac12 \,\text{days}$

The value of $(1024)^{-\dfrac {4}{5}}$ 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. $\left (\dfrac {1}{4}\right )^{3}$

  2. $\left (\dfrac {1}{4}\right )^{2}$

  3. $\dfrac {1}{256}$

  4. $\dfrac {1}{512}$

Show answer
Correct Option: C
Explanation:

$1024=2\times2\times2\times2\times2\times2\times2\times2\times2\times2 = 2^{10}$


To find,
$(1024)^{-\dfrac{4}{5}} = 2^{-\dfrac{10\times4}{5}}$ 
                   $= 2^{-8}$

$2^{8}= 2\times2\times2\times2\times2\times2\times2\times2 = 256$

$\therefore (1024)^{-\dfrac{4}{5}} = \dfrac{1}{256}$

When simplified, the product $\left( 1-\cfrac { 1 }{ 3 }  \right) \left( 1-\cfrac { 1 }{ 4 }  \right) \left( 1-\cfrac { 1 }{ 5 }  \right) ...\left( 1-\dfrac 1n \right) $ becomes

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 }{ n } $

  2. $\dfrac { 2 }{ n } $

  3. $\dfrac { 2(n-1) }{ n } $

  4. $\dfrac { 2 }{ n(n+1) } $

Show answer
Correct Option: B
Explanation:

$\left( 1-\cfrac { 1 }{ 3 }  \right) \left( 1-\cfrac { 1 }{ 4 }  \right) \left( 1-\cfrac { 1 }{ 5 }  \right) ...\left( 1- \cfrac 1n \right) =\cfrac { 2 }{ 3 } .\cfrac { 3 }{ 4 } .\cfrac { 4 }{ 5 } ....\cfrac { n-2 }{ n-1 } .\cfrac { n-1 }{ n } =\cfrac { 2 }{ n } $

$4\frac{4}{5}\div\frac{3}{5}$ of $5+\frac{4}{5}\times\frac{3}{10} -\frac{1}{5}$ is simplified, then the result 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. $1\frac{16}{25}$

  2. $1\frac{17}{25}$

  3. $\frac{40}{25}$

  4. $\frac{42}{25}$

Show answer
Correct Option: A
Explanation:

Apply BODMAS
$4\frac{4}{5}\div\frac{3}{5}$ of $5+\frac{4}{5}\times\frac{3}{10} -\frac{1}{5}$
$=\frac{24}{5}\div3+\frac{4}{5\times\frac{3}{10}-\frac{1}{5}}$
$=\frac{8}{5}+\frac{6}{25}-\frac{1}{5}$
$=\frac{41}{25}$
$=1\frac{16}{25}$
Option 'A' is the answer

$\left( 1-\dfrac {1}{3} \right) \left( 1-\dfrac {1}{4} \right) \left( 1-\dfrac {1}{5} \right) ....\left( 1-\dfrac {1}{n} \right) $ equals

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

  1. $\dfrac {1}{n}$

  2. $\dfrac {2}{n}$

  3. $\dfrac {3}{n}$

  4. $\dfrac {4}{n}$

Show answer
Correct Option: B
Explanation:

$\quad \left( 1-\cfrac { 1 }{ 3 }  \right) \left( 1-\cfrac { 1 }{ 4 }  \right) \left( 1-\cfrac { 1 }{ 5 }  \right) ...=\cfrac { 2 }{ 3 } .\cfrac { 3 }{ 4 } .\cfrac { 4 }{ 5 } ...\cfrac { n-1 }{ n } =\cfrac { 2 }{ n } $

The product of the reciprocals of $\dfrac {x + 3}{x + 2}$ and $\dfrac {x^{2} -4}{x^{2} - 9}$ 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. $\dfrac {1}{(x -3)(x - 2)}$

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

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

  4. $(x - 3)(x - 2)$

Show answer
Correct Option: C
Explanation:
The reciprocal of $\cfrac {x + 3}{x + 2}$ is $\cfrac {x + 2}{x + 3}$ 
And the reciprocal of $\cfrac {x^{2} -4}{x^{2} - 9}$ is $\cfrac {x^{2} -9}{x^{2} - 4}$
$\Rightarrow \cfrac {x^{2} -9}{x^{2} - 4} = \cfrac {(x-3)(x+3)}{(x-2)(x+2)}$
$\Rightarrow \cfrac {(x + 2)}{(x + 3)} \times \cfrac {(x - 3)}{(x - 2)}\times \cfrac {(x + 3)}{(x + 2)} = \cfrac {x - 3}{x - 2}$.

The value of $\large{\frac{1}{3}} \ of\ \large{4\frac{2}{3}}$ $\div$ $\large{2\frac{1}{3}} of\ \large{1\frac{1}{2}}$ 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. 1

  2. 2

  3. 3

  4. None of these

Show answer
Correct Option: D
Explanation:

$\large{\frac{1}{3}} \ of\ \large{4\frac{2}{3}}$ $\div$ $\large{2\frac{1}{3}} of\ \large{1\frac{1}{2}}$



$=\dfrac13\times4\dfrac23\div2\dfrac13\ of\ \dfrac12$


$=\dfrac{14}{9}\div\dfrac73\ of\ \dfrac32$


$=\dfrac{14}{9}\div\dfrac73\times\dfrac32$


$=\dfrac{14}{9}\div\dfrac72$


$=\dfrac{14}{9}\times\dfrac27$


$=\dfrac49$


$\text{option D (None of these) is correct}$

Product of $\displaystyle \frac{12}{24}$ and $\displaystyle \frac{36}{72}$ 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. $\displaystyle \frac{16}{24}$

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

  3. $4$

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

Show answer
Correct Option: D
Explanation:

Product of the fraction is $\dfrac{12}{24}$ and $\dfrac{36}{72}$ is 

$\dfrac{12}{24} \times \dfrac{36}{72} = \dfrac{432}{1728} $ 
After simplifying, $\dfrac{432}{1728}$ can also be written as $\dfrac{1}{4}$.
Hence, the answer is $\dfrac{1}{4}$.

Product of $\displaystyle\frac{11}{12}\times \frac{16}{4}\times \frac{9}{16}$ 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. $\displaystyle 2\frac{1}{16}$

  2. $\displaystyle \frac{3}{4}$

  3. $\displaystyle \frac{2}{8}$

  4. $\displaystyle \frac{9}{6}$

Show answer
Correct Option: A
Explanation:

The product of $\dfrac{11}{12} \times \dfrac{16}{4} \times \dfrac{9}{16} $ is

$=\dfrac{11\times 16\times 9}{12\times 4\times 16}=\dfrac{33}{16}$ 
This can also be written as $\dfrac{32+1}{16}=2\dfrac{1}{16}$.
Hence, the answer is $2\dfrac{1}{16}$.