Question

The sum of the numerator and denominator of a fraction is 8.if 3 is added to both numerator nd denominator the fraction becomes 3/4,find the fraction.

Pls help me with this answer...

Answer 1

✬ Fraction = 3/5 ✬

Step-by-step explanation:

Given:

• Sum of numerator and denominator of a fraction is 8.
• After adding 3 to both numerator and denominator the fraction becomes 3/4.

To Find:

• What is the fraction?

Solution: Let the numerator be n and denominator be d.

• Fraction = n/d

➼ n + d = 8

➼ d = 8 – n.........(1)

• Adding 3 to both numerator and denominator •

• New Numerator = n + 3
• New Denominator = d + 3

∴ New fraction = n/d = (n + 3)/(d + 3)

A/q

$\implies{\rm }$ (n + 3)/(d + 3) = 3/4

$\implies{\rm }$ 4(n + 3) = 3(d + 3) [ By cross multiplication ]

$\implies{\rm }$ 4n + 12 = 3d + 9

$\implies{\rm }$ 4n – 3d = 9 – 12

$\implies{\rm }$ 4n – 3d = –3........(2)

• Putting the vale of d in equation 2 from 1 ➮

➮ 4n – 3 (8 – n) = – 3

➮ 4n – 24 + 3n = – 3

➮ 7n = – 3 + 24

➮ 7n = 21

➮ n = 21/7

➮ n = 3

Therefore, Numerator = 3 and

Denominator = (8 – n) = (8–3) = 5

Hence, The Fraction is n/d = 3/5