How to Establish Proportions to Solve Missing Term Problems

Let’s learn about how to establish proportion to find missing terms. The problem that we’ll use is Hannah uses a pottery wheel to make 6 bowls in 3 hours. At the same pace, how long will it take her to make a set of 15 bowls?

What do we know? She makes 6 bowls in 3 hours. If we look at the ratio of bowls made to hours taken, what do we get? Number of bowls made is 6, hours taken is 3. That’s one ratio. Second is, we need to find out how long it will take her to make a set of 15 bowls. Let’s say, to make 15 bowls, Hannah needs ‘y’ hours. This is what we need to determine. If this is true, what is the ratio for bowls made to hours taken. In this case, bowls made would be 15 and hours taken would be ‘y’.

The question tells us that she’s working at the same pace which means this ratio and this ratio should be equivalent. If that is indeed true then 6:3 should be in proportion or equivalent to 15:y. I can write this as fraction 6/3 must be equal to 15/y if she’s working at the same pace. Let’s cross multiply which gives me 6×y=3×15 or 6y=45. If 6y=45, because it is a multiplication equation I should be able to divide both sides by 6 because that’s the number I want to remove. I want only y on the left inside. So 6/6 give me 1, so y=45/6. Let’s divide both sides by 3 which give me 15/2. The number of hours needed by Hannah or y=15/2 or 7.5 hours. In order to make 15 bowls, Hannah needs 7 ½ hours.

Let’s quickly recap what we’ve learned. What we’ve learned is in order to use proportion to find the missing term, we establish the ratios. In this case, the ratios of bowls made to hours taken were 6:3. Similarly, I can look at the second ratio which was 15:y. If there are 15:y then if this two are equivalent, 6:3 should be the same as 15=y which means 6/3 =15:y, I can cross multiply to get the answer y=15/2 or y= 7 ½ hours. In order to make 15 bowls, Hannah would need 7 ½ hours.