Question

The denominator of a fraction is 2 more than the numerator. If both denominator and numerator are increased by 1 the fraction becomes 2/3. Find the original fraction.

Answer 1

Let x = the numerator

Let x + 2 = the denominator

x + 1 = 2

x + 3 3 Cross multiply

3x + 3 = 2x + 6

x = 3

x + 2 = 5

Fraction = 3/5

Ok

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Answer 2

Step-by-step explanation:

Let,

• The numerator of fraction = x
• The denominator of a fraction = x + 2

If both denominator and numerator are increased by 1 fraction becomes 2/3

• The numerator of fraction = x + 1
• The denominator of a fraction = x + 2 + 1 = x + 3

★ According to the Question :

⇒ $\dfrac{x \: + \: 1}{x \: + \: 3} \: = \: \dfrac{2}{3}$

⇒ 3 (x + 1) = 2 (x + 3)

⇒ 3x + 3 = 2x + 6

⇒ 3x - 2x = 6 - 3

⇒ x = 3

The numerator of fraction = 3

• The denominator of a fraction = x + 2

⇒ 3 + 2

⇒ 5

The denominator of a fraction = 5

★ Fraction = $\dfrac{3}{5}$

Therefore, The original fraction is $\dfrac{3}{5}$