The number that should be added to both the numerator and denominator of 42-92 so that the fraction becomes 4-9 is

The correct option is C 36Let the number to be added be x Then 4^4+x/9^9+x=4/9⇒16+x/81+x=4/9 ⇒ 144+9x=324+4x ⇒ 9x 4x=324+4x ⇒ 9x 4x=324 144⇒ ...

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Standard IX

Mathematics

Standard Form to Normal Forms

The number th...

Question

The number that should be added to both the numerator and denominator of $\frac{4^{2}}{9^{2}}$ so that the fraction becomes $\frac{4}{9}$ is

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Solution

The correct option is C 36
Let the number to be added be x Then
$\frac{4^{4} + x}{9^{9} + x} = \frac{4}{9} \Rightarrow \frac{16 + x}{81 + x} = \frac{4}{9}$
$\Rightarrow 144 + 9 x = 324 + 4 x$
$\Rightarrow 9 x - 4 x = 324 + 4 x$
$\Rightarrow 9 x - 4 x = 324 - 144 \Rightarrow 5 x = 180$
$\Rightarrow x = \frac{180}{5} = 36$

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A fraction becomes $\frac{9}{11}$ , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$ . Find the fraction. [3 MARKS]

A fraction becomes 9/11 , 2 is added to both numerator and denominator. If 3 is added to both the numerator and denominator it becomes 5/6. Find the fraction

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The number that should be added to both the numerator and denominator of 4292 so that the fraction becomes 49 is

The correct option is C 36Let the number to be added be x Then44+x99+x=49⇒16+x81+x=49⇒144+9x=324+4x⇒9x−4x=324+4x⇒9x−4x=324−144⇒5x=180⇒x=1805=36

The number that should be added to both the numerator and denominator of $\frac{4^{2}}{9^{2}}$ so that the fraction becomes $\frac{4}{9}$ is