Final answer:
To find the ratio a:b given that a/2 = b/5, cross-multiply to find 5a=2b, and then simplify by dividing by b to get the final ratio of a:b = 2:5.
Step-by-step explanation:
To find the ratio a:b when it is given that a/2 = b/5, we can write the proportion by setting the two ratios equal to one another.
So, a/2 = b/5. We then cross-multiply to solve for the variables a and b. Multiplying both sides of the equation by 2 and 5 respectively, we get 5a = 2b. To simplify the ratio a:b, we can divide each side by 2b to isolate a on one side, resulting in a = (2b/5). We can now express a in terms of b, and represent the ratio a:b as (2b/5):b, which can be simplified further by dividing both terms by b. This leaves us with the ratio 2/5, meaning a:b=2:5.
The result tells us that for every 2 units of a, there are 5 units of b. This is an important concept in understanding how to find proportions and ratios, which are foundational in many areas of mathematics.