Question

Q1.the numerator of a rational number is 2 less than the denominator if 16 is added to the numerator the fraction become 5/3.find the fraction​.

Answer 1

Step-by-step explanation:

Answer: 19/21

Step-by-step explanation:

Let the denominator of the fraction be x.

It is given that numerator is 2 less than denominator. So,

Numerator will be (x - 2)

Now,

According to second condition,

If 16 is added to the numerator then the fraction becomes 5/3

It means,

$\begin{gathered}\frac{(x-2)+16}{x}=\frac{5}{3}\\\;\\\frac{x-2+16}{x}=\frac{5}{3}\\\;\\\frac{x+14}{x}=\frac{5}{3}\\\;\\\textbf{Cross Multiplying;}\\\;\\3(x+14)=5x\\\;\\3x+42=5x\\\;\\42=5x-3x\\\;\\42=2x\\\;\\x=\frac{42}{2}\\\;\\\textbf{x\;=\;21}\end{gathered}$

Hence,

Denominator = 21

Numerator = 21 - 2 = 19

Fraction = 19/21

Answer 2

Answer:

Let the numerator be x & denominator be y

Fraction = numerator/denominator = x/y

ATQ

CASE 1 :

x = y - 4

x- y = - 4 …………..(1)

CASE 2 :

8(x - 2) = y + 1

8x - 16 = y + 1

8x - y = 17………... (2)

On Subtracting eq (2) from (1)

x - y = - 4

8x - y = 17

(-) (+) (-)

----------------

-7x = -21

x = 21/7

x = 3

Put x = 3 in eq 1,

x - y = - 4

3 - y = - 4

y = 3 + 4 = 7

y = 7

x = 3

y = 7

Fraction = x/y = 3/7

Hence, the fraction is 3/7.

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