Tag: multiplication of a fractions

Questions Related to multiplication of a fractions

Find the value of x and y respectively.
5$\dfrac{1}{x}$ $\times y$ $\dfrac{3}{4}$ = 20

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

  1. $3, 1$

  2. $3, 3$

  3. $4, 1$

  4. $5, 3$

Show answer
Correct Option: B
Explanation:

Put x = 3 and y = 3 of LHS, we get
5$\dfrac{1}{3}$ $\times$ 3$\dfrac{3}{4}$ = $\dfrac{16}{3}$ $\times$ $\dfrac{15}{4}$ = 4 $\times$ 5 = 20

If we multiply a fraction by itself, the fraction thus obtained is $\displaystyle\frac{16}{81}$. The original fraction 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. $\displaystyle\frac{8}{27}$

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

  3. $\displaystyle 2\frac{1}{3}$

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

Show answer
Correct Option: D
Explanation:

Let the original fraction be $\dfrac{x}{y}$.

$\Rightarrow$  According to the given question,
$\Rightarrow$  $\dfrac{x}{y}\times \dfrac{x}{y}=\dfrac{16}{81}$

$\Rightarrow$  $\left(\dfrac{x}{y}\right)^2=\dfrac{16}{81}$
$\rightarrow$  Taking square root on both sides we get,
$\Rightarrow$  $\dfrac{x}{y}=\dfrac{4}{9}$

Which of the following statements is true?

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 and -1 are reciprocal of themselves.

  2. Zero has no reciprocal.

  3. The product of the two middle rational numbers is a rational number.

  4. All of these

Show answer
Correct Option: D
Explanation:

Option A

Reciprocal of a number is the number obtained by dividing it by $1$. 
Here, reciprocal of $1 = \dfrac{1}{1} = 1$ and reciprocal of $-1 = \dfrac{1}{-1} = -1$
Hence, they are both the reciprocals of themselves.

Option B
Reciprocal of $0$ can be denoted as $\dfrac{1}{0}$ which isn't defined. Anything divided by $0$ is not defined.

Option C
Addition, subtraction, multiplication or division of a rational number with another rational number always gives a rational number.

$\therefore$ All the statements are correct.

A farmer grows vegetable in his field. In $\dfrac{2}{3}$ of the field, he grows potatoes, in $\dfrac{1}{4}$ he grows onions and in the rest of the field he grows tomatoes. In what part of the field does he grow tomatoes?

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

  1. $\dfrac{1}{12}$

  2. $\dfrac{11}{12}$

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

  4. $\dfrac{1}{6}$

Show answer
Correct Option: A
Explanation:

Part of field in which potatoes are grown $= \dfrac{2}{3}$ 


Part of field in which onions are grown $= \dfrac{1}{4}$ 

$\Rightarrow$ Total part of field covered by potatoes and onions $= \dfrac{2}{3} + \dfrac{1}{4} = \dfrac{11}{12}$

$\therefore$ Remaining part of field in which tomatoes are grown $= 1 - \dfrac{11}{12} = \dfrac{1}{12}$

Which one of the following is same as $30\%$ of $40\%$ of $560$?

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

  1. $60\%$ of $40\%$ of $280$

  2. $15\%$ of $80\%$ of $280$

  3. $30\%$ of $40\%$ of $280$

  4. $15\%$ of $80\%$ of $140$

Show answer
Correct Option: A
Explanation:

30% of 40% of 560 = $\dfrac{30}{100}\ \ \times\dfrac{40}{100}\ \ \times 560\ \ = 67.2 $



Option A: 
60% of 40% of 280 = $\dfrac{60}{100}\ \ \times\dfrac{40}{100}\ \ \times 280\ \ = 67.2 $


Option B: 
15% of 80% of 280 = $\dfrac{15}{100}\ \ \times\dfrac{80}{100}\ \ \times 280\ \ = 33.6$


Option C: 
30% of 40% of 280 = $\dfrac{30}{100}\ \ \times\dfrac{40}{100}\ \ \times 280\ \ = 33.6$


Option D: 
15% of 80% of 140 = $\dfrac{15}{100}\ \ \times\dfrac{80}{100}\ \ \times 140\ \ = 16.8$


So, 30% of 40% of 560 = 60% of 40% of 280

Option A is correct





If $\dfrac{m}{n} = \dfrac{4}{3}$ and $\dfrac{r}{t} = \dfrac{9}{14}$, the value of $\dfrac{3mr - nt}{4nt - 7mr}$ 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. $-5\dfrac{1}{2}$

  2. -$ \dfrac{11}{14}$

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

  4. $\dfrac{11}{14}$

  5. none of these

Show answer
Correct Option: B
Explanation:

$\cfrac { m }{ n } =\cfrac { 4 }{ 3 } ,\cfrac { r }{ t } =\cfrac { 9 }{ 14 } \ m=\cfrac { 4n }{ 3 } ,r=\cfrac { 9t }{ 14 } \ mr=\cfrac { 6nt }{ 7 } \ 3mr-nt=\cfrac { 18nt }{ 7 } -nt=\cfrac { 11nt }{ 7 } \ 4nt-7mr=4nt-6nt=-2nt\ \cfrac { 3mr-nt }{ 4nt-7mr } =-\cfrac { 11 }{ 14 } $

In the multiplication of $\dfrac{2}{3}$ with $4$, the numerator will be :

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

  1. $2$

  2. $8$

  3. $4$

  4. $12$

Show answer
Correct Option: B
Explanation:

Given multiplication of $\dfrac{2}{3}$ with $4$

$\dfrac{2}{3}\times 4=\dfrac{2\times4}{3}=\dfrac{8}{3}$
The numerator of the fraction is $8$

If $\frac{2}{3}$  of $48$ is simplified, the answer 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. $36$

  2. $32$

  3. $30$

  4. $28$

Show answer
Correct Option: B
Explanation:

$\frac{2}{3}$  of $48$
        $=\frac{2}{3}\times48$
        $=2\times16$
        $=32$

Simplify $\frac{-39}{3}\times\frac{19}{5}\times\frac{-45}{38}$

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

  1. $\frac{117}{2}$

  2. $\frac{-117}{2}$

  3. $\frac{127}{2}$

  4. $\frac{-127}{2}$

Show answer
Correct Option: A
Explanation:

$\frac{-39}{3}\times\frac{19}{5}\times\frac{-45}{38}$
$=\frac{-13\times-9}{2}$
$=\frac{117}{2}$

Multiply $\frac{-2}{11}\times\frac{-44}{16}$

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

  1. $-2$

  2. $4$

  3. $\frac{1}{2}$

  4. $-4$

Show answer
Correct Option: C
Explanation:

$\frac{-2}{11}\times\frac{-44}{16}$
$=\frac{-1\times-4}{8}$
$=\frac{-1\times-1}{2}=\frac{1}{2}$