Question

The numerator of a rational number is 4 less than it denominator of 1 is added to both numerator and denominator is become 2 / 3 find a rational number

Answer 1

Answer:-

Let the number be x/y.

Given:

Numerator is 4 less than the denominator.

⟹ Numerator = denominator - 4

⟹ x = y - 4 -- equation (1)

And,

If 1 is added to both numerator and denominator, the number becomes 2/3.

⟹ (x + 1)/(y + 1) = 2/3

⟹ 3(x + 1) = 2(y + 1)

⟹ 3x + 3 = 2y + 2

Substitute the value of x from equation (1).

⟹ 3(y - 4) + 3 = 2y + 2

⟹ 3y - 12 + 3 = 2y + 2

⟹ 3y - 2y = 2 + 12 - 3

⟹ y = 11

Substitute the value of y in equation (1).

⟹ x = 11 - 4

⟹ x = 7

∴ The required fraction x/y is 7/11.

Answer 2

Answer:-

7/11

Step by step explanation:-

Let the denominator of rational no. be x.

Then numerator = x - 4.

Adding 1 to both numerator and denominator,

Denominator = x + 1.

Numerator = x - 4 + 1 = x - 3.

Substitution:-

↦ x - 3/x + 1 = 2/3

↦ 3(x - 3) = 2(x + 1) [∵Applying cross - multiplication]

↦ 3x - 9 = 2x + 2

↦ 3x - 2x = 2 + 9

↦ x = 11

➤ Numerator = 11 - 4 = 7

∴Required rational number = 7/11

[∵rational numbers will be in the form of a/b]