Question

THE DENOMINATOR OF A RATIONAL NUMBER IS GREATER THAN IT'S NUMERATOR BY 4. IF THE NUMERATOR AND DENOMINATOR ARE BOTH INCREASED BY 3, THE NEW FRACTION BECOMES 4/5. FIND THE ORGINAL NUMBER

Answer 1

Answer:

Let the numerator of a rational number be x then the denominator is x+8.

Therefore, Rational number = \frac{x}{x+8}

x+8

x

According to the question,

\frac{x+17}{x+8-1}=\frac{3}{2}

x+8−1

x+17

=

2

3

\Rightarrow\ \frac{x+17}{x+7}=\frac{3}{2}⇒

x+7

x+17

=

2

3

\Rightarrow\ 2\left(x+17\right)=3\left(x+7\right)⇒ 2(x+17)=3(x+7)

\Rightarrow\ 2x+34=3x+21⇒ 2x+34=3x+21

\Rightarrow\ 2x-3x=21-34⇒ 2x−3x=21−34

\Rightarrow\ -x=-13⇒ −x=−13

\Rightarrow\ x=13⇒ x=13

Hence, the required rational number

=\ \frac{x}{x+8}=\frac{13}{13+8}=\frac{13}{21}=

x+8

x

=

13+8

13

=

21

13

Step-by-step explanation:

hope this help you