Question

The numerator of a rational number is 3 less than the denominator if denominator is increased by 5 and numerator by 2 we get the rational number 1/ 2. find the rational number​

Answer 1

Answer:

4/7

Step-by-step explanation:

let the numerator be x

and denominator be y

according to frst condition

x= y-3.

x-y = -3 .......(1)

according to second condition...

$\frac{x + 2}{y + 5} = \frac{1}{2}$

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

2x+4 = y+5

2x-y= 5-4

2x-y = 1 ......(2)

solving (1) & (2) simultaneously...

x - y = -3

2x- y = 1

- + -

_________

-x = -4

x=4

substitute this value in equation (1)

x -y = -3

4 - y= -3

-y = -3-4

y= 7

thus the fraction is 4/7

Answer 2

✬ Rational Number = 4/7 ✬

Step-by-step explanation:

Given:

• Numerator of a rational number is 3 less than denominator.
• After increasing denominator by 5 and numerator by 2 we get 1/2.

To Find:

• What is the original rational number?

Solution: Let the denominator be x. Therefore,

➼ Numerator = 3 less than denominator

➼ x = (x – 3)

Now, Adding 5 to denominator and 2 to numerator new fraction will be

➼ Numerator = (x – 3 + 2)

➼ Denominator = (x + 5)

➨ Fraction = Numerator/Denominator

➨ (x – 3 + 2)/(x + 5)

A/q,

$\implies{\rm }$ (x – 3 + 2)/(x + 5) = 1/2

$\implies{\rm }$ (x – 1)/(x + 5) = 1/2

$\implies{\rm }$ 2(x – 1) = 1(x + 5)

$\implies{\rm }$ 2x – 2 = x + 5

$\implies{\rm }$ 2x – x = 5 + 2

$\implies{\rm }$ x = 7

So,

➱ Denominator of fraction is x = 7

➱ Numerator of fraction is (x – 3)

=> (7 – 3) = 4

Hence, The fraction or rational number is Numerator/Denominator = 4/7