Question

The denominator of a fraction is 7 more than the numerator. If 1 is
added to the numerator and 6 is added to the denominator, the value of
the fraction will be 1⁄2.Find the numerator and the denominator.

Answer 1

Step-by-step explanation:

X IS NUMERATOR

X+7 IS IS DENOMINATOR

Answer 2

Answer :-

• Numerator = 11

• Denominator = 18

Given :-

• The denominator of a fraction is 7 more than the numerator.

• If we add 1 to the numerator and 6 to it's denominator the value of fraction will be ½.

To Find :-

• The value of numerator and denominator.

Step By Step Solution :-

Let us consider the value of numerator be x.

Then the denominator will be x + 7.

Now, Equation will be ⤵

$\boxed{ \tt{ \purple{ \cfrac{x + 1}{x + 7 + 6} = \cfrac{1}{2} }}}$

Now, Let us solve the given equation to find the value of x.

$\implies \sf\cfrac{x + 1}{x + 7 + 6} = \cfrac{1}{2} \\ \\ \implies \sf \cfrac{x + 1}{x + 13} = \cfrac{1}{2} \\ \\ \implies \sf2(x + 1) = 1(x + 13) \\ \\ \implies \sf2x + 2 = x + 13 \\ \\ \implies \sf2x - x = 13 - 2 \\ \\ \implies \sf \: x = 11$

Therefore the value of x = 11

Now value of numerator = 11 and the value of denominator = x + 7 => 18

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