Question

when we added 6 to the numerator of a fraction and simplify it we get 1/2.when we add 7 to the denominator of same fraction and simplify fraction we get 1/3 what is the original fractions​

Answer 1

Answer:

Original fraction is 19/50.

Step-by-step explanation:

let the fraction be x/y ;

x+6/y = 1/2

cross multiplication,

2x+12= y............(i)

x/y+7= 1/3

cross multiplication,

3x = y+7

3x = 2x + 12 +7. ( putting eqñ 1 value)

3x- 2x = 19

x= 19

Putting value of x in eqñ 1;

2(19)+12= y

38 +12= y

50= y

So the original franction is 19/50.

Answer 2

Answer:

The original fraction is 19/50.

Step-by-step explanation:

Given :-

• When we add 6 to the numerator of a fraction and simplify it, we get 1/2.
• When we add 7 to the denominator of the same fraction and simplify it, we get 1/3.

To find :-

• The Original fraction.

Solution :-

Let the numerator of the fraction be x and the denominator of the fraction be y.

According to the 1st condition ,

$\implies \sf \: \dfrac{x + 6}{y} = \dfrac{1}{2} \\ \\ \implies \sf \: y \: = 2x + 12..............(i)$

According to the 2nd condition,

$\implies \sf \: \dfrac{x}{y + 7} = \dfrac{1}{3} \\ \\ \implies \sf \: 3x = y + 7 \\ \\ \implies \sf \: 3x = 2x + 12 + 7 \: \{put \: y \: = \: 2x + 12 \: from \: eq(i) \} \\ \\ \implies \sf \: 3x - 2x = 19 \\ \\ \implies \sf \: x = 19$

Then,

• Numerator of the fraction = 19

Now put x = 19 in eq (I).

y = 2x + 12

→ y = 2×19 + 12

→ y = 50

• Denominator of the fraction= 50

Therefore,

• The Original fraction = 19/50.