Question

denominator of rational number that is greater than it's numerator by 7.if the numerator is increased by 17 and the denominator is decreased by 6 ,the new number becomes 2 find the area of the plate​

Answer 1

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

Answer 2

Answer:

Let the fraction be qp

So q=p+7

q−6p+17=2

⇒p+7−6p+17=2

⇒p+1p+17=2

⇒p+17=2p+2

⇒p=15

q=15+7=22

So qp=2215.

hope it will help