Question

19. The sum of the numerator and the denominator of a fraction is 18. If the
denominator is increased by 2, the fraction reduces to 1/3. Find the
numerator of the fraction.​

Answer 1

✬ Fraction = 5/13 ✬

Step-by-step explanation:

Given:

• Sum of numerator and denominator is 18.
• After increasing denominator by 2 , fraction reduces to 1/3.

To Find:

• What is the numerator of fraction ?

Solution: Let the numerator be x and denominator be y. Therefore, Fraction will be x/y.

➟ Numerator + Denominator = 18

➟ x + y = 18

➟ x = 18 – y......(1)

[ Now, Adding 2 to denominator ]

• New denominator = y + 2
• New fraction = x/y + 2

A/q

• After increasing denominator by 2 , fraction reduces to 1/3.

$\implies{\rm }$ x/y + 2 = 1/3

$\implies{\rm }$ 3(x) = 1(y + 2)

$\implies{\rm }$ 3x = y + 2

$\implies{\rm }$ 3(18 – y) = y + 2

$\implies{\rm }$ 54 – 3y = y + 2

$\implies{\rm }$ 54 – 2 = y + 3y

$\implies{\rm }$ 52 = 4y

$\implies{\rm }$ 52/4 = y

$\implies{\rm }$ 13 = y

So,

➬ Denominator is y = 13

➬ Numerator is x = 18 – 13 = 5

Hence, the original fraction is x/y = 5/13

Answer 2

EXPLANATION.

Let the numerator of fraction be = x

Let the denominator of fraction be = y

Find the numerator of a fraction.

Case = 1

The sum of numerator and the denominator

of a fraction = 18

=> x + y = 18 ......(1)

Case = 2

if the denominator is increased by 2

the fraction reduces to 1/3

=> x / y + 2 -1/3 = 0

=> x / y + 2 = 1/3

=> 3x = y + 2

=> 3x - y = 2 ....(2)

From equation (1) and (2) we get,

=> 4x = 20

=> x = 5

put the value of x = 5 in equation (1)

we get,

=> 5 + y = 18

=> y = 13

Fraction = x/y = 5/13