Tag: dividing fractions

Questions Related to dividing fractions

Evaluate: $\dfrac{(3\dfrac{2}{3})^{2} -(2\dfrac{1}{2})^{2}}{(4\dfrac{3}{2})^{2} -(3\dfrac{1}{3})^{2}}$ $\div$ $\dfrac{3\dfrac{2}{3} -2\dfrac{1}{2}}{4\dfrac{3}{2} -3\dfrac{1}{3}}$

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

  1. $\dfrac{35}{53}$

  2. $\dfrac{37}{53}$

  3. $\dfrac{42}{59}$

  4. $\dfrac{47}{60}$

Show answer
Correct Option: B
Explanation:

$\dfrac{(3\frac{2}{3})^2-(2\frac{1}{2})^2}{(4\frac{3}{2})^2-(3\frac{1}{3})^2} \div \dfrac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$


$=\dfrac{(3\frac{2}{3}+2\frac{1}{2})(3\frac{2}{3}-2\frac{1}{2})}{(4\frac{3}{2}+3\frac{1}{3})(4\frac{3}{2}-3\frac{1}{3})} \div \dfrac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$

$=\dfrac{3\frac{2}{3}+2\frac{1}{2}}{4\frac{3}{2}+3\frac{1}{3}}$

$=\dfrac{\dfrac{11}{3}+\dfrac{5}{2}}{\dfrac{11}{2}+\dfrac{10}{3}}$

$=\dfrac{\dfrac{22+15}{6}}{\dfrac{33+20}{6}}$

$=\dfrac{37}{53}$

Solve $\left[\dfrac{170}{3} +\dfrac{6}{7}\right] \div \left[\dfrac{2}{7} \times \dfrac{11}{2}\right]$

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

  1. $\dfrac{1208}{3\times 11}$

  2. $\dfrac{1208}{11}$

  3. $\dfrac{1208}{3}$

  4. $\dfrac{1208}{9\times 11}$

Show answer
Correct Option: A
Explanation:

$\left[\dfrac{170}{3} +\dfrac{6}{7}\right] \div \left[\dfrac{2}{7} \times \dfrac{11}{2}\right]$


$=\left[ \dfrac{1190+18}{21}\right] \div \left[ \dfrac{11}{7}\right]$


$=\left[ \dfrac{1190+18}{21}\right] \times \left[ \dfrac{7}{11}\right]$

$=\left[ \dfrac{1208}{11\times 3}\right]$

Divide the difference of $\dfrac{1}{5}$ and $\dfrac{2}{7}$ by $\dfrac{2}{7}$.

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

  1. $\dfrac{1}{10}$

  2. $\dfrac{21}{10}$

  3. $\dfrac{3}{10}$

  4. $\dfrac{4}{10}$

Show answer
Correct Option: C
Explanation:

Difference of  $\dfrac{1}{5}$  and $\dfrac{2}{7}$ is  


$\dfrac{2}{7} - \dfrac{1}{5} = \dfrac{2\times5 - 1\times7}{35} =\dfrac{10 - 7}{35} =\dfrac{3}{35}$

Now divide $\dfrac{3}{35}$  by $\dfrac{2}{7}$  

we have, $\dfrac{3}{35}÷\dfrac{2}{7} =\dfrac{3}{35}\times \dfrac{7}{2} =\dfrac{3}{10}$

Ans: $\dfrac{3}{10}$

Simplify $35\times 6\dfrac{1}{14}$(approximately)$=$

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

  1. $220.5$

  2. $220$

  3. $212$

  4. $231$

Show answer
Correct Option: C
Explanation:
$6 \cfrac{1}{14} = \cfrac{14 \times 6 + 1}{14} = \cfrac{85}{14}$
$\therefore \; 35 \times 6\cfrac{1}{14} = 35 \times \cfrac{85}{14} = \cfrac{5 \times 85}{2} = \cfrac{425}{2} = 212.5 \approx 212$
Hence, 212 is the correct answer.

A ribbon of length $5\dfrac{1}{4}$m is cut in to small pieces each of length $\dfrac{3}{4}$ m number of pieces will be

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

  1. $5$

  2. $6$

  3. $7$

  4. $8$

Show answer
Correct Option: C
Explanation:

$ \Rightarrow  $ let length l $ = 5\dfrac{1}{4}$ m 

$ l = 5+\dfrac{1}{4} = \dfrac{21}{4}m $

& Small n pieces of length $ x = \dfrac{3}{4}$m 

So, $ l = nx $

$ n = \dfrac{l}{x} = \dfrac{21}{4}\times \dfrac{4}{3} = 7 $

So, there are 7 pieces of length $ \dfrac{3}{4} $

The unit digit of $2017^{2017}$.

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

  1. $7$

  2. $9$

  3. $3$

  4. $1$

Show answer
Correct Option: A
Explanation:

Consider the unit digits of $7^{x}$ series which is $7,9,3,1$

These four digits go on repeat So consider Remainder of ${2017}\div{4}=1$
so unit digit is $7$

If $Rs.510$ be divided among $A,B,C$ in such a way that $A$ gets $\dfrac{2}{3}$ of what $B$ gets and $B$ gets $\dfrac{1}{4}$ of what $C$ gets, then their shares are respectively:

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

  1. $Rs.120, Rs.240, Rs.150$

  2. $Rs.60, Rs.90, Rs.360$

  3. $Rs.150, Rs.300, Rs.60$

  4. $None\ of\ these$

Show answer
Correct Option: B
Explanation:
$A=\dfrac{2}{3}B$

$B=\dfrac{1}{4}C$

$\Rightarrow C=4B$

$A+B+C=510$                                            

$=2B/3+B+4B=510$
                               
$=2B+3B+12B=510\times 3$                      

$=17B=510\times 3$ 
                                             
$B=30\times 3=90$

$A=\dfrac{2\times 90}{3}$

$=60$

 $C=4\times 90$

$=360$.

Evaluate: 

$(5 \div 2.25) \div (9 \div 2.25)$.

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

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

  2. $\dfrac{100}{9}$

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

  4. $1$

Show answer
Correct Option: A
Explanation:

$ \dfrac {\dfrac {5}{2.25}}{\dfrac {9}{2.25}} = \dfrac {5}{9}$

Simplify : $\displaystyle \frac{2+2\times 2}{2\div 2\times 2}\div \frac{\frac{1}{2}\div \frac{1}{2} \, \text{of} \, \frac{1}{2}}{\frac{1}{2}+\frac{1}{2} \, \text{of} \, \frac{1}{2}}$

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

  1. $1$

  2. $2$

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

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

Show answer
Correct Option: D
Explanation:

Given exp =$\displaystyle =\frac{2+4}{1\times 4}\div \frac{\frac{1}{2}\div \frac{1}{4}}{\frac{1}{2}+\frac{1}{4}}$
$\displaystyle =\frac{6}{2}\div\frac{\frac{1}{2}\times \frac{4}{1}}{\frac{3}{4}}=3\div \frac{2}{\frac{3}{4}} $
$\displaystyle =3\div \frac{8}{3}=3\times \frac{3}{8}=\frac{9}{8}=1\frac{1}{8}$

Find the value of $ \cfrac{2}{3}\times \cfrac{3}{\tfrac{5}{6}\div \tfrac{2}{3} \, \text {of} \, \,1\tfrac{1}{4}}$

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

  1. $2$

  2. $1$

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

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

Show answer
Correct Option: A
Explanation:

Given expression

$ \cfrac{2}{3}\times \cfrac{3}{\tfrac{5}{6}\div \tfrac{2}{3} \, \text {of} \, \,1\tfrac{1}{4}}$

$=\displaystyle \frac{2}{3}\times\dfrac{3}{\tfrac{5}{6}\div \left ( \tfrac{2}{3}\times\tfrac{5}{4} \right )}$


$\displaystyle=\frac{2}{3}\times\dfrac{3}{\tfrac{5}{6}\div \tfrac{5}{6}}=\frac{2}{3}\times\frac{3}{1}=2$