##### 5.2 Proportions

You have been typing a paper for your literature class. If you can write 3 pages in one hour, how much can you write in 4 hours? Assuming that each page contains 600 words, how many words will you be able to type in 4 hours? How will you solve this problem then? You can easily answer this by using ratios, rates or proportions.

In this chapter, we will be discussing just that. In the first segment of this chapter we will be looking at ratios. A ratio is simply the relationship between numbers, like in the given situation above, the ratio is 3 pages: 1 hour, x pages: 4 hours. Note that ratio isn’t just applicable in mathematics, as you know, there are plenty of applications everywhere like the Golden Ratio in Art, and the Golden Triangle in Architecture.

Later this chapter, we will be discussing about rates. Rate is a special ratio that tells us the speed at which something is done, the amount of work done in a particular time.

We can use rates to solve the second question: How many words will you be able to type in 4 hours given that you can type 600 words per page?

In the case of the problem above, your rate would be 1800 words per hour. In this segment, we will also be discussing about unit rate and unit price. Both of them are simply rates, except that they both have a denominator of 1. In the problem given above, our unit rate is 1800 words per hour.

Now to be able to get the total amount of words and pages you will end up typing in 4 hours, you will be using proportion. Proportion is simply the relationship between a pair of ratio. In this relationship, it tells us that two ratios are equal to each other. So in that case, we will use 3:1 = x:4, and 1800:1 = x:4 to solve for the pages and words respectively. How will we do that? We are simply going to cross multiply. Do you know the answers now?

### Proportions

Everyone has somehow seen and used proportions before, such as baking recipes and maps. Proportion is basically another way to say two ratios or rates are equal. We can represent proportions in two ways: in the form of fraction (a/b = c/d) and using a colon (a:b = c:d).