Tag: division of a fraction

Questions Related to division of a fraction

What is the simplified value of $\displaystyle \frac{\frac{1}{3}\div \frac{1}{3}\times\frac{1}{3}}{\frac{1}{3}\div \frac{1}{3}of\frac{1}{3}}-\frac{1}{9}?$

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

  1. $0$

  2. $2$

  3. $\dfrac{1}{9}$

  4. $\dfrac{2}{9}$

Show answer
Correct Option: A
Explanation:

(Using BODMAS)
$\displaystyle \frac{\frac{1}{3}\div \frac{1}{3}\times \frac{1}{3}}{\frac{1}{3}\div \frac{1}{3}of\frac{1}{3}}-\frac{1}{9}=\frac{\frac{1}{3}\times \frac{3}{1}\times \frac{1}{3}}{\frac{1}{3}\div \frac{1}{9}}-\frac{1}{9}$
$\displaystyle =\frac{1\times \frac{1}{3}}{\frac{1}{3}\times \frac{9}{1}}-\frac{1}{9}=\frac{1}{3\times 3}-\frac{1}{9}=\frac{1}{9}-\frac{1}{9}=0$

Sunny was given $\displaystyle \frac{1}{3}$ of a sum of money and Ankur was given $\displaystyle \frac{1}{3}$ of what was left. What is Ankur's share as a fraction of Sunny's Share?

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

  1. $\displaystyle \frac{2}{9}$

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

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

  4. $\displaystyle \frac{1}{9}$

Show answer
Correct Option: C
Explanation:
Sunny gives $\dfrac { 1 }{ 3 }$ of his money
Left amount will be $ 1-\dfrac { 1 }{ 3 } = \dfrac { 2 }{ 3 }$ 
Amount received by Ankur is $\dfrac { 1 }{ 3 }$ of left amount $(\frac { 2 }{ 3 }$  of total amount $)$ 
Amount received by Ankur will be $\dfrac { 1 }{ 3 } \times \dfrac { 2 }{ 3 }$ of total amount $= \dfrac { 2 }{ 9 }$ of total amount
Ankur's share as a fraction of Sunny's share is $\dfrac{\frac{2}{9}}{\frac{1}{3}}=\dfrac{2}{3}$
So Correct answer will be option C

If we multiply a fraction by itself and divide the product by its reciprocal the fraction thus 
obtained is $\displaystyle 18\frac{26}{27}$. The original fraction is 

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

  1. $\displaystyle \frac{8}{27}$

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

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

  4. None of these

Show answer
Correct Option: B
Explanation:

$Let\quad fraction\quad x\quad then\ x\times x\div \dfrac { 1 }{ x } =18\dfrac { 26 }{ 27 } =\dfrac { 512 }{ 27 }$


 $x\times x\times \dfrac { x }{ 1 } =\dfrac { 512 }{ 27 } \ we\quad get\quad x=\dfrac { 8 }{ 3 } =2\dfrac { 2 }{ 3 } $
So correct answer will be option B

Find the value of $\displaystyle \frac{2}{1+\frac{1}{1-\frac{1}{2}}}\times\frac{3}{\frac{5}{6}of\frac{3}{2}\div 1\frac{1}{4}}$

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

  1. $2$

  2. $5$

  3. $6$

  4. $1$

Show answer
Correct Option: A
Explanation:

$\displaystyle \frac{2}{\displaystyle1+\frac{1}{\displaystyle1-\frac{1}{\displaystyle2}}}\times\frac{3}{\displaystyle\frac{5}{\displaystyle6}of\frac{3}{\displaystyle2}\div 1\frac{1}{\displaystyle4}}$
$=\displaystyle \frac{2}{\displaystyle1+\frac{1}{\displaystyle\frac{1}{\displaystyle2}}}\times\frac{3}{\displaystyle\frac{15}{\displaystyle12}\div \frac{5}{\displaystyle4}}$

$=\displaystyle\frac{2}{\displaystyle1+2}\times\frac{3}{\displaystyle\frac{15}{\displaystyle12}\times\frac{4}{\displaystyle5}}=\frac{2}{\displaystyle3}\times\frac{3}{\displaystyle1}=2$

When any number is divided by 1, the quotient is

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

  1. 1

  2. 0

  3. 2

  4. number itself

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Correct Option: D
Explanation:

Any number  divided by 1 equals that number.
for eg:
$8 \div 1 = 8$
$10 \div 1 = 10$
$\therefore $When any number is divided by 1, the quotient is number itself.
Option D is correct.

Simplify : $\displaystyle \left [ 3\frac{1}{4}\div \left { 1\frac{1}{4}-\frac{1}{2}\left ( 2\frac{1}{2}-\frac{1}{4}-\frac{1}{6} \right ) \right } \right ]\div \left ( \frac{1}{2}of4\frac{1}{3} \right )$

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

  1. 18

  2. 36

  3. 39

  4. 78

Show answer
Correct Option: B
Explanation:

Given exp.
$\displaystyle =\left [ \frac{13}{4}\div \left { \frac{5}{4}-\frac{1}{2}\left ( \frac{5}{2}-\frac{3\, \, \,2}{2} \right ) \right } \right ]\div \left ( \frac{1}{2}of\frac{13}{3} \right )$
$\displaystyle =\left [ \frac{13}{4}\div \left { \frac{5}{4}-\frac{1}{2}\left ( \frac{5}{2}-\frac{1}{12} \right ) \right } \right ]\div \frac{13}{6} $
$=\displaystyle \left [ \frac{13}{4}\div \left { \frac{5}{4}-\frac{1}{2}\times \frac{30-1}{12} \right } \right ]\div \frac{13}{6}$
$\displaystyle =\left [ \frac{13}{4}\div \left { \frac{5}{4}-\frac{29}{24} \right } \right ]\div \frac{13}{6}$
$\displaystyle =\left [ \frac{13}{4}\div \frac{30-29}{24} \right ]\div \frac{13}{6}$
$\displaystyle =\left ( \frac{13}{4} \div \frac{1}{24}\right )\div \frac{13}{4}=\frac{13}{4}\times 24\times \frac{6}{13}=36$

If $2805\,\div\, 2.55\, =\, 1100\,, then\, 280.5\,\div\,25.5\, =\,$ .............

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

  1. 1.1

  2. 1.01

  3. 0.11

  4. 11

Show answer
Correct Option: D
Explanation:

$\displaystyle\frac{280.5}{25.5}\,=\, \frac{280.5}{25.5}\,\times\, \frac{10}{10}\,\times\, \frac{10}{10}$

$=\,\displaystyle\frac{2805}{2.55}\,\times\,\frac{1}{100}$

$=\,\displaystyle\frac{1100}{100}\,=\, 11$

$143.6\, \div\, 2000\, =\,..........$

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

  1. 0.1718

  2. 7.18

  3. 0.718

  4. 0.0718

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Correct Option: D
Explanation:

$143.6\div 200=71.8\div100=0.0718$

 Hence the answer is option is D

15 of $\displaystyle \frac{1}{5}$ is

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

  1. $\displaystyle \frac{1}{75}$

  2. $\displaystyle \frac{151}{5}$

  3. 3

  4. -3

Show answer
Correct Option: C
Explanation:

15 of $\displaystyle \frac{1}{5}\, =\, 15\, \times\, \displaystyle \frac{1}{5}\, =\, 3$

If $\sqrt{5}=2.236$ and $\sqrt{10}=3.162$, the value of $\displaystyle\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}$ on simplifying is

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

  1. 0.455

  2. 0.855

  3. 0.655

  4. 0.755

Show answer
Correct Option: C
Explanation:

values of $\sqrt { 5 } $ and $\sqrt { 10 } $ are given.

as per problem,
$\frac { \sqrt { 10 } -\sqrt { 5 }  }{ \sqrt { 2 }  } $
$\frac { 3.162-2.236 }{ 1.414 } $(value of $\sqrt { 2 } $ is1.414)
$\frac { 0.926 }{ 1.414 } $
$0.655$