Question

The denominator of a fraction is 5 more than its numerator . If 2 is subtracted from both the numerator and the denominator , the fraction becomes 4/5 . Find the fraction.

Answer 1

Answer:

6/7

Step-by-step explanation:

denominator of fraction=5

numerator =?

so,2 is sub from 4/5

2- 4/5=

FIRST, add 2+4,2+5=

6,7 therefore, answer is 6/7

Answer 2

Answer:

$\bigstar{\bold{The\:fraction=\dfrac{22}{27}}}$

Step-by-step explanation:

$\Large{\underline{\bf{Given:}}}$

• Denominator of a fraction is 5 more than the numerator
• If 2 is subtracted from both the numerator and denominator the fraction becomes 4/5

$\Large{\underline{\bf{To\:Find:}}}$

• The fraction

$\Large{\underline{\bf{Solution:}}}$

➝ Here we have to find the fraction.

➝ Let us assume the numerator of the fraction as x.

➝ Hence by given,

    Denominator = 5 + Numerator

    Denominator = 5 + x

➝ Hence the fraction is given by,

    $\sf The\:fraction=\dfrac{x}{x+5}$

➝ By given subtracting 2 from both the numerator and denominator the fraction becomes 4/5.

➝ Hence,

    $\sf \dfrac{x-2}{x+5-2} =\dfrac{4}{5}$

    $\sf \dfrac{x-2}{x+3} =\dfrac{4}{5}$

➝ Cross multiplying we get,

    5 (x - 2) = 4 (x + 3)

    5x - 10 = 4x + 12

    5x - 4x = 12 + 10

    x = 22

➝ Hence the numerator of the fraction is 22.

➝ Now finding the denominator,

    Denominator = x + 5 = 22 + 5 = 27

➝ Hence the denominator of the fraction is 27.

➝ Therefore the fraction is 22/27.

    $\boxed{\bold{The\:fraction=\dfrac{22}{27}}}$

$\Large{\underline{\bf{Verification:}}}$

➝ Denominator = 5 + Numerator

    27 = 22 + 5

    27 = 27

➝ If 2 is subtracted from both numerator and denominator, the fraction becomes 4/5.

    $\sf \dfrac{22-2}{27-2} =\dfrac{4}{5}$

    $\sf \dfrac{20}{25} =\dfrac{4}{5}$

    $\sf \dfrac{4}{5} =\dfrac{4}{5}$

Hence verified.