Question

The numerator of a rational number is 4 less than its denominator .If 1 is added to both numerator and denominator, it becomes 2/3 find the rational number
Please answer fast

Answer 1

Given: The numerator of a rational number is 4 less than its denominator. & If 1 is added to both numerator and denominator, the rational number becomes ⅔.

❍ Let the denominator of the rational no. be n and the numerator of the rational no. be (n – 4).

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${\underline{\underline{\bigstar\;{\boldsymbol{ According\;to\;the\; question\::}}}}}$

• If 1 is added to both numerator and denominator, the rational number becomes ⅔.

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$:\implies\sf\quad \Bigg\{\dfrac{Numerator + 1}{Denominator + 1}\Bigg\} = \Bigg\{\dfrac{2}{3}\Bigg\}$

$:\implies\sf\quad \Bigg\{\dfrac{n - 4 + 1}{n + 1}\Bigg\}= \Bigg\{\dfrac{2}{3}\Bigg\}$

$:\implies\sf\quad \Bigg\{\dfrac{n - 3}{n + 1}\Bigg\}= \Bigg\{\dfrac{2}{3}\Bigg\}$

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

$:\implies\sf\quad 3n - 9 = 2n + 2$

$:\implies\sf\quad 3n - 2n = 2 + 9$

$:\implies\quad{\pmb{\sf{ n = 11}}}$

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★ T h e⠀N u m b e r :

$\qquad\bullet\sf\: Denominator\; of\;no.= 11$

$\qquad\bullet\sf\: Numerator\;of\;no. = (11 - 4) = 7$

$\therefore{\underline{\sf{The\; required\;rational\; number\; is\;\pmb{\sf{\dfrac{7}{11}}}.}}}$

Answer 2

Answer:

Given :-

The numerator of a rational number is 4 less than its denominator .If 1 is added to both numerator and denominator, it becomes 2/3

To Find :-

Fraction

Solution :-

Let the numerator be x

Denominator = x + 4

x + 1/x + 4 + 1 = 2/3

3(x + 1) = 2(x + 4 + 1)

3(x + 1) = 2(x + 5)

3x + 3 = 2x + 10

3x - 2x = 10 - 3

x = 7

Finding denominator

x + 4 » 7 + 4

11

Fraction = 7/11