The denominator of a fraction is 7 more than its numerator. If '1' is subtracted from both the numerator and the denominator, it becomes $\frac{9}{6}$. Form an equation to find the value of the actual fraction.

Given :

The denominator of a fraction is 7 more than its numerator.

If '1' is subtracted from both the numerator and the denominator, it becomes $\frac{9}{6}$.

To do :

We have to form an equation to find the value of the actual fraction.

Solution :

Let the numerator of the fraction be 'x'.

The denominator $= x + 7 $.

Then the actual fraction is $\frac{x}{x+7}$.

 '1' is subtracted from both the numerator and the denominator.

$\frac{x -1}{x+7 - 1} =\frac{9}{6} $

$\frac{x -1}{x+6} =\frac{9}{6} $

Cross multiply,

$6(x-1) = 9(x+6)$

$6x -6 = 9x + 54$

$6x - 9x = 54+6$

$-3x = 60$

$x = \frac{60}{-3} = -20$

$\frac{x}{x+7} = \frac{-20}{-20+7} = \frac{-20}{-13}$

The actual fraction is $\frac{-20}{-13}$.

Therefore, the equation to find the actual fraction is $\frac{x -1}{x+6} =\frac{9}{6} $.

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Updated on: 10-Oct-2022

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