Question

if two is added to the numerator and denominator it becomes 9/10 and if subtract from the numerator and denominator it becomes 4/5 from the fraction

Answer 1

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Correction as below :-

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions.  

Step :- 1

Let the fraction  be x/y

Step :- 2

Given ,

If 2 is added to numerator and denominator it becomes 9/10

(x + 2)/( y + 2 ) = 9/10

⇒ 10 ( x +2 ) = 9 ( y+2 )

⇒ 10x + 20 = 9y + 18

⇒  10x - 9y + 20 - 20 = 18 - 20.

⇒ 10x - 9y = -2 ------->>> 1

Step :-3

If 3 is Subtract from both numerator and denominator it becomes 4/5

(x - 3 )/( y - 3 ) = 4/5

⇒ 5 ( x - 3 ) = 4 ( y - 3 )

⇒ 5x - 15 = 4y - 12

⇒  5x – 4y – 15 = 4y – 4y – 12  

⇒ 5x – 4y – 15 + 15 = – 12 + 15

⇒ 5x - 4y = 3 ------->>> 2

So , we have 10x - 9y = -2 ------>>> 3

5x - 4y = 3 ------->>> 4

Step :-4

Multiply both side by equation ( 4 ) by (2) We get ,

10x - 8y = 6 ----------->>> 5

Solving Equation (3) and (5) we get ,

$10x - 9y = -2 \\\\10x - 8y = 6 \\\\============\\\\-y = -8$

y = 8

Step :- 5

For finding value of x Substitute the value of y in equation (4)

5x -  4y = 3

⇒ 5x - 4 (8) =3

⇒ 5x - 32 = 3

Add 32 both side

⇒ 5x - 32 + 32 = 3 + 32

⇒ 5x = 35

⇒ x = 35/7

⇒ x =7

Therefore the fraction is 7/8

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Answer 2

Answer:

7divided by 8

Step-by-step explanation: