Question

the numerator of a fràction is 6 less than the denominator . if 3 is added to the numerator the fràction is equal to 2/3. whàt is the original fraction​

Answer 1

Answer:

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Answer 2

Given :

• Numerator of a fraction is 6 less than the denominator

• If 3 is added to the numerator the fraction is equal to 2/3

To find :

• Original fraction

Solution :

Let the fraction be (x - 6)/x -----(1)

where,

• x - 6 is the numerator

• x is the denominator

According to the first condition in the question :-

→ Adding 3 to the numerator :

$\\ \implies \sf \dfrac{(x - 6) + 3}{x} = \dfrac{2}{3}$

$\\ \implies \sf \dfrac{x - 6 + 3}{x} = \dfrac{2}{3}$

$\\ \implies \sf 3(x - 3) = 2x$

$\\ \implies \sf 3x - 9 = 2x$

$\\ \implies \sf 3x - 2x = 9$

$\\ \implies \sf x = 9$

The value of x = 9

Substitute the value of x in equation (1) :-

→ ( x - 6 ) / x

→ ( 9 - 6 ) / 9

→ 3 / 9

→ 1/3

Therefore, the original fraction = 1/3