Question

If the numerator of a fraction is multiplied by 2 and its denominator is increased by 1, it becomes 1. however if the numerator is increased by 4 and denominator is multiplied by 2, the fraction becomes 1/2 find the numbers

Answer 1

let the fraction be " X / Y

according to question ,

first activity,

X ×2 / Y + 1 = 1

2X / Y + 1 = 1

2X = Y + 1

2X - Y = 1. ----------(eq.(1)

second activity ,

( X + 4 ) / Y ×2 = 1 / 2


(X + 4 )/ 2Y = 1/ 2

X + 4 = Y

X - Y = - 4 --------eq.(2)

now subtract equation (2) from equation (1) , we get,

X = 1 -(-4)

X = 1+ 4 = 5

X = 5

from(1)

- Y = 1 - 2(5)

- Y = -9

Y = 9

hence the fraction( number ) is X / Y = 5 / 9

★hope it helps ★