Question

9. The denominator of a fraction is greater than the numerator by 4. If both the denominator and numerator are increased by 5, the new fraction is 2/3. Find the original fraction.​

Answer 1

Step-by-step explanation:

Given:-

Given:-the denominator of a fraction is greater than the numerator by 4 .if both the denominator and numerator are increased by 5, the new fraction is 2/3 .

To find:-

find the original fraction

Solution:-

Let the numerator be X

then, The denominator=X+4

if both the denominator and numerator are increased by 5, the new fraction is 2/3

=>(X+5)/(X+4+5)=2/3

=>(X+5)/(X+9)=2/3

applying cross multiplication then

=>3(X+5)=2(x+9)

=>3X+15=2X+18

=>3X-2X=18-15

=>X=3

=>X+4=3+4=7

Answer:-

The numerator =3

The denominator=7

The original fraction =3/7

Answer 2

Step-by-step explanation:

Let numerator of the fraction = x

Denominator of the fraction = y

y = x + 4 ⸻➤eq 1 (.given )

new fraction, numerator will be = x - 5

and Denominator = y + 5

x - 5 / y + 5 = 2/3

3( x- 5 ) = 2 ( y + 5 )

3x - 15 = 2y + 10

from equation 1 we put the value of y .

3 x - 2 y = 15 + 10

3 x - 2 ( x + y ) = 25

3x - 2x + 8 = 25

1x + 8 = 25

x = 25 - 8

x = 17 ⸻➤ eq ( 2 )

from equation 1 and 2 ..

we get

y = 17 + 4

y = 21

• numerator/ Denominator
• 17 / 21 ( original fraction)

hope it helps you..