Tag: maths

Questions Related to maths

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

Show answer
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 } $
$0.655$

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

Show answer
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

Show answer
Correct Option: D
Explanation:

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

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

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

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

Show answer
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. $\dfrac{8}{9}$

Show answer
Correct Option: A
Explanation:

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


So, option A is correct.