Learn About Missing Terms in Equivalent Ratios Let’s learn about how we find missing terms when we are given an equivalent ratio or set of ratios. There are two problems. The first one wants to find the value of ‘a’ if we are given that 2a:5 and 6:20 are in proportion. Let’s do this one first. We are given that 2a:5 and 6:20, these two ratios are in proportion. When I say in proportion, it means they are equal or equivalent. That means they are equivalent. So, let’s write this in a different way. If 2a:5 is written as 2a/5 is the equivalent of 6:20, all I did was replace the way of writing the ratio instead of 6:20, we were down 6 by 20 or 6/20 and 2a/5. If these two are in proportion, that means 2a/5=6/20. Now that I have this equation, I can simply cross multiply the two. Let’s create a little bit of space and look at cross multiplying. So, 2a/5 cross multiplied by 6/20 means 2a*20=6*5. I just cross multiplied, or 2a*20 is 40*a=30. So, if we need to solve for a, let’s divide both sides by 40 which will give me 40/40 is 1, so a=30/40. Now since this is improper fraction, I can express this in simplest forms by dividing both sides by 10 which gives me ¾. So, if these two ratios are in proportion, then a=3/4. That is the answer we were looking for. Now, let’s solve the second problem. It says that the ratio of the number of male and female workers in a textile, male is 5:3 so number of male workers to the number of female workers is 5:3. If there are 115 male workers we need to find the number of female workers. So for the second or the b problem, we know that the ratio of male workers to female workers is 5:3. We know that the number of male worker equals 115. So, let’s say that the number of female workers equals y. So now, what do we know? We know that the ratio is 5:3 which is male is to female. And in reality, there are 115 and y. So, which means 5:3 and 115:y are in proportion which now what we can do, if 5:3 and 115:y are in proportion, that means 5/3 is equivalent or equal to 115/y. I just expressed the ratios in a different format. So by cross multiplying, what we get is 5*y=3*115, so 5y=3*115 is 345. So, in order to solve for y, this is a multiplication equation, so let’s divide both sides by five, 5y/5 which gives me y on the left inside equals 345/5 which is 69. So, y=69 or the number of female workers equals 69. Quickly recapping what we’ve learned. If two ratios are given to us and they are in proportion, that means that they are equal when expressed as ratios. So, 2a:5 can be expressed as 2a/5 and 6:20 can be expressed as 6/20 and if these are in proportion that means those two fractions are equal. If these two fractions are equal then I can cross multiply to find the answer for a which is ¾. Similarly, if we are given that the number of male and female workers in a textile mill is in the ratio of 5:3 and we’re given the number of male workers 115 and the number of female workers we assume as y, that gives us the second ratio. So, these two ratios are equivalent or in proportion than 5/3=115/y which means I can cross multiply to get the answer that y=69.