The denominator of a rational number is greater than its numerator by

1.	The denominator of a rational number is greater than its numerator by 6 .if the numerator is increased by 15 and denominator by 1 then the obtained number is 3 by 2 find the rational number
Answer» ONG>⇒ GIVEN: The DENOMINATOR of a rational NUMBER is greater than its numerator by 6. When the numerator is increased by 15 and denominator by 1 then the obtained rational number is 3/2. ⇒ To Find: The rational number. ⇒ Solution: Let the numerator of the number be x. This means that the denominator of the rational number is x + 6. $\sf{\implies\:Rational\:number=\dfrac{x}{x+6}}$ It is given that that when the numerator is increased by 15 and the denominator by 1, the rational number is 3/2. $\sf{\implies\:\dfrac{x+15}{x+6+1}=\dfrac{3}{2}}$ $\sf{\implies\:\dfrac{x+15}{x+7}=\dfrac{3}{2}}$ Doing cross multiplication: $\sf{\implies\:2(x+15)=3(x+7)}$ $\sf{\implies2x+30=3x+21}$ $\sf{\implies\:30-21=3x-2x}$ $\sf{\implies\:x=9}$ This means that, → The numerator of the rational number is x which is 9. → The denominator of the rational number is x + 6 which is 15. The required rational number is 9/15. Rational Number: A number in the form p/q where p and q are integers and q ≠ 0 is termed as a rational number. Rational NUMBERS were discovered by the mathematician Pythagoras.

The denominator of a rational number is greater than its numerator by 6 .if the numerator is increased by 15 and denominator by 1 then the obtained number is 3 by 2 find the rational number

Answer» ONG>⇒ GIVEN:

The DENOMINATOR of a rational NUMBER is greater than its numerator by 6.

When the numerator is increased by 15 and denominator by 1 then the obtained rational number is 3/2.

⇒ To Find:

The rational number.

⇒ Solution:

Let the numerator of the number be x. This means that the denominator of the rational number is x + 6.

$\sf{\implies\:Rational\:number=\dfrac{x}{x+6}}$

It is given that that when the numerator is increased by 15 and the denominator by 1, the rational number is 3/2.

$\sf{\implies\:\dfrac{x+15}{x+6+1}=\dfrac{3}{2}}$

$\sf{\implies\:\dfrac{x+15}{x+7}=\dfrac{3}{2}}$

Doing cross multiplication:

$\sf{\implies\:2(x+15)=3(x+7)}$

$\sf{\implies2x+30=3x+21}$

$\sf{\implies\:30-21=3x-2x}$

$\sf{\implies\:x=9}$

This means that,

→ The numerator of the rational number is x which is 9.

→ The denominator of the rational number is x + 6 which is 15.

The required rational number is 9/15.

Rational Number:

A number in the form p/q where p and q are integers and q ≠ 0 is termed as a rational number. Rational NUMBERS were discovered by the mathematician Pythagoras.

The denominator of a rational number is greater than its numerator by 6 .if the numerator is increased by 15 and denominator by 1 then the obtained number is 3 by 2 find the rational number

Rational Number:

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