Tag: maths

Questions Related to maths

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}}$

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


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

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

Show answer
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.