The numerator of a fraction is 5 less than the denominator. If 9 is ad

1.	The numerator of a fraction is 5 less than the denominator. If 9 is added to both numerator and denominator . if become 2/3 . find the fraction.
Answer» ✬ Fraction = 1/6 ✬ Step-by-step explanation: Given: NUMERATOR of a fraction is 5 less than denominator. After adding 9 to both the fraction becomes 2/3. To Find: What is the original fraction ? Solution: Let numerator be x and denominator be y. Therefore, ➟ Fraction = Numerator/denominator ➟ Fraction = x/y Also, ➟ x = y – 5.........i [ Now adding 9 to both ] New numerator = x + 9 New denominator = y + 9 A/q New fraction = 2/3 $\implies{\rm }$ x + 9/y + 9 = 2/3 $\implies{\rm }$ 3(x + 9) = 2(y + 9) $\implies{\rm }$ 3x + 27 = 2y + 18 $\implies{\rm }$ 3x – 2y = 18 – 27 $\implies{\rm }$ 3(y – 5) – 2y = – 9 $\implies{\rm }$ 3y – 15 – 2y = – 9 $\implies{\rm }$ y = – 9 + 15 $\implies{\rm }$ y = 6 So, fraction is Denominator = 6 Numerator = 6 – 5 = 1 Hence, original fraction was 1/6.

The numerator of a fraction is 5 less than the denominator. If 9 is added to both numerator and denominator . if become 2/3 . find the fraction.

Answer»

✬ Fraction = 1/6 ✬

Step-by-step explanation:

Given:

To Find:

Solution: Let numerator be x and denominator be y. Therefore,

➟ Fraction = Numerator/denominator

➟ Fraction = x/y

Also,

➟ x = y – 5.........i

[ Now adding 9 to both ]

A/q

$\implies{\rm }$ x + 9/y + 9 = 2/3

$\implies{\rm }$ 3(x + 9) = 2(y + 9)

$\implies{\rm }$ 3x + 27 = 2y + 18

$\implies{\rm }$ 3x – 2y = 18 – 27

$\implies{\rm }$ 3(y – 5) – 2y = – 9

$\implies{\rm }$ 3y – 15 – 2y = – 9

$\implies{\rm }$ y = – 9 + 15

$\implies{\rm }$ y = 6

So, fraction is

Hence, original fraction was 1/6.