Question

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.
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Answer 1

✬ 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.

Answer 2

Answer:

✯ Given :-

• The numerator of a fraction is 5 less than the denominator. When 9 is added to both numerator and denominator it becomes ⅔ .

✯ To Find :-

• What is the original fraction.

✯ Solution :-

» Let, the denominator be x

» And, the numerator be (x - 5)

» So, the fraction will be $\dfrac{x - 5}{x}$

➣ According to the question,

⇒ $\dfrac{(x - 5) + 9}{x - 9}$ = $\dfrac{2}{3}$

⇒ $\dfrac{x + 4}{x + 9}$ = $\dfrac{2}{3}$

⇒ 3(x + 4) = 2(x + 9)

⇒ 3x + 12 = 2x + 18

⇒ 3x - 2x = 18 - 12

⇒ x = 6

➟ Hence, the original fraction is,

↦ $\dfrac{x - 5}{x}$

↦ $\dfrac{6 - 5}{6}$

➥ $\dfrac{1}{6}$

$\therefore$ The original fraction will be $\boxed{\bold{\small{\dfrac{1}{6}}}}$

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