Question

The numerator of a fraction is 5 less than its denominator. If 1 is added to each its

Answer 1

Answer:  4/9

Step-by-step explanation:

Let x represent the denominator. Then the fraction is: (x - 5)/x

Add 1 to the numerator and denominator   →     (x - 5 + 1)/(x + 1) = 1/2

Cross Multiply:                   1(x + 1) = 2(x - 4)

Distribute:                             x + 1 = 2x - 8

Subtract x from both sides:       1 = x - 8

Add 9 to both sides:                  9 = x

Numerator:  x - 5    →     9 - 5 = 4

Denominator:  x     →     9

So the fraction is: 4/9

Answer 2

Given :-

• The numerator of a fraction is 5 less than its denominator
• If 1 is added to each its value becomes 1/2

To Find :-

• The original fraction

Solution :-

Let,

• Denominator of the fraction be “x”
• Numerator of the fraction be “x - 5”

★ If 1 is added,

• Denominator of the fraction = x + 1
• Numerator of the fraction = (x - 5) + 1

A. T. Q :-

$:\implies\tt\frac{x - 5 + 1}{x + 1} = \frac{1}{2}$

$:\implies\tt\frac{x - 4}{x + 1} = \frac{1}{2}$

$:\implies\tt 2x - 8 = x + 1$

$:\implies\tt 2x - x = 1 + 8$

$:\implies\tt x = 9$

∴ Denominator of the fraction = 9

∴ Numerator of the fraction = x - 5 = 9 -5 = 4

Thus, the fraction is $\bf\frac{4}{9}$