Question

16. numerator of rational number is 4 less than its denominator if 1 added to both is numerator and denominator the fraction before 1/2
find the fraction​

Answer 1

Given:

• Numerator of rational number is 4 less than its denominator.
• If 1 added to both is numerator and denominator the fraction before ½.

⠀⠀⠀

To find:

• Fraction?

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Solution:

⠀⠀⠀

☯ Let the Denominator of a rational be x.

Then, numerator = (x - 4)

⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\bigstar\:{\underline{\sf{According\:to\:the\:question\::}}}$

• If 1 added to both is numerator and denominator the fraction before ½.

⠀⠀⠀

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

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

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

$:\implies\sf 2x - 6 = x + 1$

$:\implies\sf 2x - x = 1 + 6$

$:\implies{\underline{\boxed{\sf{\purple{x = 7}}}}}\;\bigstar$

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Therefore,

⠀⠀⠀

• Denominator of rational number, x = 7
• Numerator of rational number, (x - 4) = 7 - 4 = 3

$\therefore\;{\underline{\sf{The\; required\;rational\;number\;is\; \bf{\dfrac{3}{7}}.}}}$

Answer 2

Answer:

Given :-

• Numerator of rational number is 4 less than its denominator. If 1 is added to both the numerator and denominator the fraction before $\dfrac{1}{2}$.

To Find :-

• What is the required fraction.

Solution :-

Let, the denominator be x

And, the numerator be x - 4

According to the question,

⇒ $\dfrac{(x - 4) + 1}{x + 1}$ = $\dfrac{1}{2}$

⇒ 2{(x - 4) + 1} = x + 1

⇒ 2x - 8 + 2 = x + 1

⇒ 2x - x = 1 + 8 - 2

➠ x = 7

Hence, the required fraction will be,

↦ $\dfrac{x - 4}{x}$

↦ $\dfrac{7 - 4}{7}$

➥ $\dfrac{3}{7}$

$\therefore$ The required fraction will be $\boxed{\bold{\small{\dfrac{3}{7}}}}\star$.