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

Answer:

3/7

Step-by-step explanation:

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Answer 2

Let the denominator of fraction be x and Numerator of fraction be y.

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$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: According\: to \: the \: Question :}}}}}\mid}$

⠀⠀⠀⠀☯ Denominator of fraction is 4 more than its Numerator.

$:\implies\sf Denominator = 4 + Numerator$

$:\implies\sf y = 4 + x\qquad\qquad\bigg\lgroup\bf eq.\;(1)\bigg\rgroup$

$\sf Original\; Fraction = \dfrac{x}{y}$

$\qquad:\implies\sf \dfrac{x}{4 + x}\qquad\qquad\bigg\lgroup\bf From\;eq.\;(1)\bigg\rgroup$

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⠀⠀⠀⠀☯ After subtracting 1 from each Numerator and denominator the fraction became 1/2.

After subtracting 1,

• Numerator = (x - 1)

• Denominator = (y - 1)

★ Fraction after subtracting 1 from Numerator and Denominator,

$:\implies\sf \dfrac{x - 1}{y - 1} = \dfrac{1}{2}$

$:\implies\sf \dfrac{x - 1}{(4 + x) - 1} = \dfrac{1}{2}$

$:\implies\sf \dfrac{x - 1}{x + 3} = \dfrac{1}{2}$

$:\implies\sf 2(x - 1) = x + 3$

$:\implies\sf 2x - 2 = x + 3$

$:\implies\sf 2x - x = 3 + 2$

$:\implies{\boxed{\frak{\pink{x = 5}}}}\;\bigstar$

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Therefore, value Numerator and Denominator is,

• Numerator, x = 5

• Denominator, y = (x + 4) = 5 + 4 = 9

$\therefore$ Hence, The original fraction became $\bf \dfrac{5}{9}$.