Question

14. The denominator of a fraction is two more than its numerator. If one is added to
both, then the fraction reduces to 4/5Find the original fraction​

Answer 1

$\sf\pink{Given :-}$

• The denominator of a fraction is two more than its numerator.
• If one is added to both, then the fraction reduces to 4/5.

$\sf\green{To \ find :-}$

• Find the original fraction.

$\sf\orange{Solution :-}$

• Let the Numerator be x and denominator be x + 2.

One is added to both then the fraction will be

⇝Numerator = x + 1

⇝Denominator = x + 2 + 1 = x + 3

So, x + 1 / x + 3 = 4 / 5

⟹ 5 ( x + 1 ) = 4 ( x + 3 )

⟹ 5x + 5 = 4x + 12

⟹ 5x - 4x = 12 - 5

⟹ x = 7

• x = 7

So , the original fraction will be ,

↬x / x + 2

↬ 7 / 7 + 2

↬ 7 / 9

$\tt{original \ fraction \ will \ be \ 7 / 9 }$

Answer 2

Given:-

• The denominator of a fraction is two more than its numerator.
• If one is added to both, then the fraction reduces to 4/5.

To find:-

• original fraction.

Solution:-

• Let the Numerator be x and denominator be x + 2.
• One is added to both then the fraction will be

Numerator = x + 1

Denominator = x + 2 + 1 = x + 3

⠀⠀⠀

⠀

$\begin{gathered} \sf \implies x + 1 / x + 3 = 4 / 5 \: \: \: \: \: \\ \\ \: \sf \implies5 ( x + 1 ) = 4 ( x + 3 ) \\ \\ \: \: \: \: \: \sf \implies5x + 5 = 4x + 12 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies5x - 4x = 12 - 5 \\ \\ \sf \implies \: x = 7 \\ \\ \: \: \: \: \: \: \: \: \: \implies\underline{\boxed{\rm{\pink x = 7}}}\end{gathered}$

So , the original fraction will be ,

↬x / x + 2

↬ 7 / 7 + 2

↬ 7 / 9

$\boxed{ \sf{ \pink{original\: fraction\: will\: be\: 7/9}}}$