Question

the denominator of a fraction is 4 more than its numerator on subtract 1 from each numerator and denominator the fraction became 1/2 find the original fraction​

Answer 1

✬ Original Fraction = 5/9 ✬

Step-by-step explanation:

Given:

• Denominator of a fraction is 4 more than numerator.
• After subtracting 1 from both numerator and denominator fraction becomes 1/2.

To Find:

• What is original fraction ?

Solution: Let the numerator of fraction be x. Therefore,

➟ Denominator = 4 more than x

➟ Denominator = (x + 4)

∴ Original fraction = Numerator/Denominator

• x/(x + 4)

[ Now subtracting 1 ]

• New numerator = (x – 1)
• New denominator = (x + 4 – 1)

A/q

• After subtracting 1 from both numerator and denominator fraction becomes 1/2.

$\implies{\rm }$ (x – 1)/(x + 4 – 1) = 1/2

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

$\implies{\rm }$ 2(x – 1) = 1(x + 3)

$\implies{\rm }$ 2x – 2 = x + 3

$\implies{\rm }$ 2x – x = 3 + 2

$\implies{\rm }$ x = 5

So,

➛ Numerator of fraction is x = 5

➛ Denominator of fraction is 5 + 4 = 9

∴ Original fraction = 5/9

Answer 2

Answer:

Let the Numerator be a and Denominator be (a + 4) of the fraction respectively.

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf \dfrac{Numerator-1}{Denominator-1}=\dfrac{1}{2}\\\\\\:\implies\sf \dfrac{a - 1}{(a + 4) - 1} = \dfrac{1}{2}\\\\\\:\implies\sf \dfrac{a - 1}{a + 3} = \dfrac{1}{2}\\\\\\:\implies\sf 2(a - 1) = a + 3\\\\\\:\implies\sf 2a - 2 = a + 3\\\\\\:\implies\sf 2a - a = 3 + 2\\\\\\:\implies\sf a = 5$

⠀

$\dag\:\underline{\boxed{\sf Original\:Fraction=\dfrac{a}{(a+4)}=\dfrac{5}{9}}}$