Tag: part number

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

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

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.

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

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

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

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

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

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

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

$\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 }  } $
$=\frac { 1.732-1.4142+1 }{ 2.8284 } =0.466$
                                               $(\sqrt { 3 } =\frac { \sqrt { 6 }  }{ \sqrt { 2 }  } =\frac { 2.4495 }{ 1.4142 } =1.732)$

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

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

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