Question

the denominator of a rational number is greater than its numerator by 3. if three is subtracted from the numerator and 2 is added to its denominator the new number is 1/5 . find the number​

Answer 1

✬ Number or Fraction = 5/8 ✬

Step-by-step explanation:

Given:

• Denominator of a rational number is greater than its numerator by 3.
• After subtracting 3 from the numerator and adding 2 to the denominator the number becomes 1/5.

To Find:

• What is the number?

Solution: Let the numerator be x. Then the denominator will be (x + 3)

➟ Fraction = x/(x + 3)

[ Subtracting 3 from the numerator ]

• New numerator = (x – 3)

[ Adding 2 to the denominator ]

• New denominator = x + 3 + 2 = x + 5

∴ New fraction = New numerator/new denominator

➟ New Fraction = (x – 3)/(x + 5)

A/q

$\small\implies{\sf }$ (x – 3)/(x + 5) = 1/5

$\small\implies{\sf }$ 5 (x – 3) = 1(x + 5)

$\small\implies{\sf }$ 5x – 15 = x + 5

$\small\implies{\sf }$ 5x – x = 5 + 15

$\small\implies{\sf }$ 4x = 20

$\small\implies{\sf }$ x = 20/4

$\small\implies{\sf }$ x = 5

So,

➨ Numerator = x = 5

➨ Denominator = (x + 3) = 5+3 = 8

Hence, The original fraction = N/D = 5/8

Answer 2

$\bf\large{\underline{Question :- }}$

the denominator of a rational number is greater than its numerator by 3. if three is subtracted from the numerator and 2 is added to its denominator the new number is 1/5 . find the number.

$\bf\large{\underline{Solution :- }}$

• Let the numerator be = x

† Denominator is greater then it's numerator by 3

• So, denominator be = x + 3

† According to Question †

• if 3 is subtracted from numerator and 2 is added to to its denominator we get new no. 1/5

$\bf\large{\underline{So,}}$,

→ Numerator be = x - 3

→ Denominator be = x + 3 + 2

Now,

$\rm\large → \frac{x - 3}{x + 3 + 2} = \frac{1}{5}$

$\rm → 5 ( x - 3 ) = 1 ( x + 3 + 2 )$

$\rm → 5 x - 15 = x + 5$

$\rm → 5x - x = 5 + 15$

$\rm → 4x = 20$

$\rm → x = \frac{20}{4}$

$\rm\large → x = 5$

• † Above we consider numerator = x
• denominator = x + 3

$\bf\large{\underline{So,}}$

• x = 5 ( Numerator )
• x + 3 = 5 + 3 = 8 ( Denominator )

$\</strong><strong>b</strong><strong>f\large{\underline</strong><strong>{</strong><strong>Hence</strong><strong>,}}$

• The the numerator is 5 and denominator is 8.

$\</strong><strong>b</strong><strong>f\large{\underline{</strong><strong>Therefore</strong><strong>,}}$

• the Original fraction was = 5/8