Question

D) The denominator of a rational number is greater than its numerator by 3.If the
numerator is increased by 1 and denominator is increased by 3, the number obtained is
$\frac{1}{2}$
Find the rational number.
​

Answer 1

Answer:

$\sf The \: rational\: number \: is \: \dfrac{4}{7}$

Given:

• The denominator of a rational number is 3 more than it's numerator.
• If numerator is increased by 1, and denominator is increased by 3, we get 1/2

To Find:

• The rational number

Solution:

Let the numerator = x

Let the denominator = y

⠀

The number becomes x/y

⠀

According to the question

⠀y = x + 3 ...( 1 )

⠀

According to the question:

⟹⠀$\sf \: \dfrac{x + 1}{y + 3} = \dfrac{1}{2}$

⠀

From ( 1 )

⟹⠀$\sf \dfrac{x + 1}{(x + 3) + 3} = \dfrac{1}{2}$

⠀

⟹⠀$\sf \dfrac{x + 1}{x + 6} = \dfrac{1}{2}$

⠀

⟹⠀$\sf 2(x + 1) = x + 6$

⠀

⟹⠀$\sf 2x + 2 = x + 6$

⠀

⟹⠀$\sf 2x - x = 6 - 2$

⠀

⟹⠀$\sf x = 4$

⠀

The numerator = x = 4

The denominator = (x + 3) = (4 + 3) = 7

$\sf The \: fraction \: is \: \dfrac{4}{7}$⠀⠀⠀⠀⠀⠀⠀

Answer 2

Answer:

here's ur answer dude

Step-by-step explanation:

Therationalnumberis

7

4

Given:

The denominator of a rational number is 3 more than it's numerator.

If numerator is increased by 1, and denominator is increased by 3, we get 1/2

To Find:

The rational number

Solution:

Let the numerator = x

Let the denominator = y

⠀

The number becomes x/y

⠀

According to the question

⠀y = x + 3 ...( 1 )

⠀

According to the question:

⟹⠀\sf \: \dfrac{x + 1}{y + 3} = \dfrac{1}{2}

y+3

x+1

=

2

1

⠀

From ( 1 )

⟹⠀\sf \dfrac{x + 1}{(x + 3) + 3} = \dfrac{1}{2}

(x+3)+3

x+1

= 21

⟹⠀\sf \dfrac{x + 1}{x + 6} = \dfrac{1}{2}

x+6

x+1

=

2

1

⠀

⟹⠀\sf 2(x + 1) = x + 62(x+1)=x+6

⠀

⟹⠀\sf 2x + 2 = x + 62x+2=x+6

⠀

⟹⠀\sf 2x - x = 6 - 22x−x=6−2

⠀

⟹⠀\sf x = 4x=4

⠀

The numerator = x = 4

The denominator = (x + 3) = (4 + 3) = 7

\sf The \: fraction \: is \: \dfrac{4}{7} Thefractionis

7

4

hope it helps