Question

the numerator of a fraction is less than its denominator by 8 . when one is added to the numerator and 2 is subtracted from the denominator the fraction obtained is 2/7. find the original fraction

Answer 1

Hey !!

Let denominator of fraction be X.

Numerator = ( X - 8 )

Fraction = Numerator/Denominator = ( X -8)/X.

According to question,

When 1 is added to numerator and 2 is subtracted from denominator the fraction obtained is 2/7.



X - 8 + 1 / X - 2 = 2/7

X - 7 / X - 2 = 2/7

7 ( X - 7 ) = 2 ( X - 2 ).

7X - 49 = 2X - 4.

7X - 2X = -4 + 49

5X = 45

X = 9.

Denominator of fraction = X = 9.

And,

Numerator of fraction = X - 8 = 9-8 = 1.

Fraction = Numerator / Denominator = 1/9

Answer 2

STEP 1: Find the fraction in term of x:

Let the denominator be x

The numerator = x - 8

$\text{Fraction = }\dfrac{x-8}{x}$

,

STEP 2: Find fraction after adding to numerator and subtracting from denominator:

1 is added to the numerator and 2 is subtracted from the denominator:

$\text{Fraction = }\dfrac{x-8 +1}{x -2}$

.

STEP 3: Equate the fraction:

The fraction is equal = 2/7:

$\dfrac{x-8 +1}{x -2} = \dfrac{2}{7}$

$\dfrac{x-7}{x -2} = \dfrac{2}{7}$

.

STEP 4 : Solve x:

$\dfrac{x-7}{x -2} = \dfrac{2}{7}$

cross multiply:

$7(x - 7) = 2(x - 2)$

distribute 7 and 2:

$7x - 49 = 2x - 4$

Combine like terms:

$5x = 45$

Divide both sides by 5:

$x = 9$

.

STEP 5: Find the fraction:

$\text{Fraction = }\dfrac{x-8}{x} = \dfrac{9 - 8}{9 } = \dfrac{1}{9}$

.

$\text {Answer = } \dfrac{1}{9}$