Tag: division of a fraction

Questions Related to division of a fraction

The value of $\displaystyle\frac{1}{\sqrt{3}+\sqrt{2}-1}$ on simplifying upto 3 decimal places, given that $\sqrt{2}=1.4142$ and $\sqrt{6}=2.4495$ is

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

  1. 0.166

  2. 0.366

  3. 0.466

  4. 0.566

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Correct Option: C
Explanation:

$\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } -1 } $
$=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ \left( \sqrt { 3 } +\left( \sqrt { 2 } -1 \right)  \right) \left( \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  \right)  } Multiplying\sqrt { 3 } -\left( \sqrt { 2 } -1 \right) \quad with\quad numerator\quad and\quad denominator\quad $
$=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ 3-{ \left( \sqrt { 2 } -1 \right)  }^{ 2 } } $
 $=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ 3-{ \left( 2+1-2\sqrt { 2 }  \right)  } } $
 $=\frac { \sqrt { 3\quad  } -\sqrt { 2 } +1 }{ 2\sqrt { 2 }  } $
$=\frac { 1.732-1.4142+1 }{ 2.8284 } =0.466$
                                               $(\sqrt { 3 } =\frac { \sqrt { 6 }  }{ \sqrt { 2 }  } =\frac { 2.4495 }{ 1.4142 } =1.732)$

Place value chart is extended on .............. side to provide place for fractions

maths fractions dividing fractions division of a fractions division of a fraction

  1. right

  2. left

  3. no

  4. None of these

Show answer
Correct Option: A
Explanation:

That is the role of the decimal point. The decimal point separates the place values that are whole values on the left from the place values that are fractional parts on the right.

So option A is the correct answer.

If $\displaystyle 2805\div 2.55=1100$ then $\displaystyle 280.5\div 25.5=$ _______

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

  1. 1.1

  2. 1.01

  3. 0.11

  4. 11

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Correct Option: D
Explanation:

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

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

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

The fraction $\displaystyle \frac{9}{4}$ can be written as

maths fractions dividing fractions division of a fractions division of a fraction

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

  2. $\displaystyle \dfrac{\dfrac{9}{4}}{1}$

  3. $\displaystyle \dfrac{\dfrac{9}{5}}{\dfrac{4}{5}}$

  4. $\displaystyle \dfrac{\dfrac{7}{6}}{\dfrac{9}{4}}$

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Correct Option: A,B,C
Explanation:
$ \dfrac{\dfrac{9}{2}}{\dfrac{4}{2}} = \dfrac{9}{2} \div \dfrac 42 =\dfrac 92 \times \dfrac 24  = \dfrac 94$

$ \dfrac{\dfrac{9}{4}}{1} = \dfrac{9}{4} \div 1 = \dfrac 92 \times 1 = \dfrac 94$

$ \dfrac{\dfrac{9}{5}}{\dfrac{4}{5}} = \dfrac{9}{5} \div \dfrac 45 =\dfrac 95 \times \dfrac 45  = \dfrac 94$

So, options $A, B$ and $C$ are correct.

Which of the following is complex fraction?

maths fractions dividing fractions division of a fractions division of a fraction

  1. $\dfrac{6\dfrac{1}{3}}{9}$

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

  3. $\dfrac{5}{9}$

  4. $\dfrac{8}{9}$

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Correct Option: A
Explanation:

$\dfrac{6\dfrac{1}{3}}{9}$ is complex fraction.


So, option A is correct.

Divide $\dfrac35$ by $4$.

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

  1. $\dfrac{12}5$

  2. $\dfrac3{20}$

  3. $\dfrac{12}{20}$

  4. $\dfrac35$

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Correct Option: B
Explanation:
According to problem

$ \dfrac{3}{5}  \div 4$

$  = \dfrac{3}{5} \times \dfrac14$

$=  \dfrac3{20} $

So option $B $ is correct

Divide $\dfrac{25}{36}$ by $5$.

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

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

  2. $\dfrac{25}{6}$

  3. $\dfrac{5}{36}$

  4. $\dfrac{36}{5}$

Show answer
Correct Option: C
Explanation:

Given that 

divide $\dfrac{25}{36} $ by $5$, writing the expression

$\dfrac{25}{36}  \div 5$

$ = \dfrac{25}{36}  \times  \dfrac15$

$ = \dfrac{5}{36}  $

So option $C $ is correct

Divide $\dfrac45$ by $2$.

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

  1. $\dfrac25$

  2. $\dfrac15$

  3. $\dfrac85$

  4. None of these

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Correct Option: A
Explanation:

$\dfrac{4}{5} \div 2 = \dfrac{\dfrac{4}{5}}{2} = \dfrac{4}{10}$


On simplifying, dividing numerator and denominator by $2$, we get $\dfrac{2}{5}$

If we divide $1$ by a fraction $x$, we get ______ $x$.

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

  1. same fraction as

  2. reciprocal of

  3. double of

  4. half of

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Correct Option: B
Explanation:

Every number has a reciprocal except 0 $(\dfrac{1}{0}$ is undefined$)$. The reciprocal is shown as $\dfrac{1}{x}$. 


When we multiply a number by its reciprocal we get $1$

$\Rightarrow$ If we divide $1$ by $x$, we get reciprocal of $x$.

Divide $10$ by $\dfrac{20}{19}$.

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

  1. $\dfrac{19}{2}$

  2. $\dfrac{1}{20}$

  3. $\dfrac{19}{20}$

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

Show answer
Correct Option: A
Explanation:
According to problem
$10$   $\div \dfrac{20}{19}$

$  = 10 \times \dfrac{19}{20}$
$=  \dfrac{19}2 $