Question

the denominator of a fraction is greater than its numerator by 12 if the numerator is decreased by 2 and the denominator is increased by 7 the new fraction is equivalent with 1/2 find the fraction

Answer 1

Let the numerator be X.

Then Denominator = x+12

A/Q

x-2/x+12+7 = 1/2

x-2/x+19=1/2

By cross multiplication

1(x+19) =2(x-2)

x+19=2x-4

19+4=2x-x

23 = x.

So, numerator = 23

Denominator= 23 +12

=35

Fraction=23/35 .

Answer 2

HeYo mate !

$<big><b>The step wise explanation :-</big></b>$

Let the numerator be 'x' .

So , denominator = x + 12 .

Given , on decreasing numerator by 2 = x-2

And , denominator = (x+12) + 7 = x + 12 + 7 = x+19

Now , the new fraction = 1/2

ATQ ,

$\frac{x - 2}{x + 19} = \frac{1}{2}$

By cross multiplying ,

$= > 1(x + 19) = 2(x - 2) \\ \\ = > x + 19 = 2x - 4 \\ \\ = > x - 2x = - 19 - 4 \\ \\ = > - x = - 23 \\ \\ (both \: sides \: minus \: gets \: cancelled) \\ \\ = > x = 23$


So the original fraction =

Numerator = 23
Denominator = 23+12 = 35

Thus , the fraction =

$= \frac{23}{35}$


HOPE HELPS !!