To make the ratio 1:3 equal to 5:9, the same value must be added to each term of the ratio.
Let's denote the value to be added as "x".
So, the new ratio becomes (1 + x) : (3 + x).
To make this new ratio equal to 5:9, we need to solve the equation:
(1 + x) : (3 + x) = 5 : 9
Cross-multiplying, we get:
9(1 + x) = 5(3 + x)
Expanding and simplifying:
9 + 9x = 15 + 5x
Rearranging the equation:
9x - 5x = 15 - 9
4x = 6
Dividing both sides by 4:
x = 6/4
Simplifying:
x = 3/2
Therefore, to make the ratio 1:3 equal to 5:9, the value 3/2 must be added to each term of the ratio.