Question

The denominator of a fraction is 2 more than the numerator.If 1 be added to both the fraction reduces to 4/5.Find the fraction​

Answer 1

$\huge\red{❥︎}\mathfrak\red{ANSWER}$

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

$\huge\mathbb\green{Solution:−}$

Let the numerator of fraction be "n"

Let the denominator of fraction be "d"

Original fraction :

➠ n \ d ⚊⚊⚊⚊ ⓵

Given that , the denominator of a fraction is two more than its numerator

So,

➜ d = n + 2 ⚊⚊⚊⚊ ⓶

Adding 1 to numerator :

➜ n + 1 ⚊⚊⚊⚊ ⓷

Adding 1 to denominator :

➜ d + 1 ⚊⚊⚊⚊ ⓸

Also given that , If one is added to both then the fraction reduces to 4/5

Thus,

From ⓷ & ⓸

➜ n + 1 \ d + 1 = 4\5

➜ 5(n + 1) = 4(d + 1)

➜ 5n + 5 = 4d + 4

➜ 5n - 4d = 4 - 5 ⚊⚊⚊⚊ ⓹

⟮ Putting d = n + 2 from ⓶ to ⓹ ⟯

➜ 5n - 4(n + 2) = 4 - 5

➜ 5n - 4n - 8 = -1

➜ n = -1 + 8

➜ n = 7 ⚊⚊⚊⚊ ⓺

Hence the numerator is 7

⟮ Putting n = 7 from ⓺ to ⓶ ⟯

➜ d = n + 2

➜ d = 7 + 2

➜ d = 9 ⚊⚊⚊⚊ ⓻

Hence the denominator is 9

⟮ Putting n = 7 from ⓺ & d = 9 from ⓻ to equation ⓵ ⟯

➜ n \ d

➨ 7 \ 9

Hence the original fraction is 7 \ 9 ..

$\huge\{\colorbox{Pink}{Hope its help you ♡︎}$

Answer 2

Answer:

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 of fraction be "n"

Let the denominator of fraction be "d"

Original fraction :

=> n \ d (1)

Given that , the denominator of a fraction is two more than its numerator

So,

=>> d = n + 2 (2)

Adding 1 to numerator :

=>> n + 1(3)

Adding 1 to denominator :

=>> d + 1 (4)

Also given that , If one is added to both then the fraction reduces to 4/5

Thus,

From 3 & 4

=>> n + 1 \ d + 1 = 4\5

=>> 5(n + 1) = 4(d + 1)

=>> 5n + 5 = 4d + 4

=>> 5n - 4d = 4 - 5 ⚊⚊⚊⚊ ⓹

⟮ Putting d = n + 2 from ⓶ to ⓹ ⟯

=>> 5n - 4(n + 2) = 4 - 5

=>> 5n - 4n - 8 = -1

=>> n = -1 + 8

=>> n = 7 ⚊⚊⚊⚊ ⓺

Hence the numerator is 7

⟮ Putting n = 7 from ⓺ to ⓶ ⟯

=>> d = n + 2

=>> d = 7 + 2

=>> d = 9 ⚊⚊⚊⚊ ⓻

Hence the denominator is 9

⟮ Putting n = 7 from ⓺ & d = 9 from ⓻ to equation ⓵ ⟯

=>> n \ d

=>>> 7 \ 9

Hence the original fraction is 7 \ 9.