Ratios and proportions are also used in business when dealing with money. For example, a business might have a ratio for the amount of profit earned per sale of a certain product such as $2.50:1, which says that the business gains $2.50 for each sale. The business can use proportions to figure out how much money they will earn if they sell more products. If the company sells ten products, for example, the proportional ratio is $25.00:10, which shows that for every ten products, the business will earn $25. These are proportional since both ratios divide into the same number: 2.50 / 1 = 2.5 and 25 / 10 = 2.5, also.
Using Ratios and Proportions
Just like these examples show, you can use ratios and proportions in a similar manner to help you solve problems. If a problem asks you to write the ratio for the number of apples to oranges in a certain gift basket, and it shows you that there are ten apples and 12 oranges in the basket, you would write the ratio as 10:12 (apples:oranges).
If the problem continues and asks you to make the gift basket three times bigger while maintaining the proportion of apples to oranges, you can do this by multiplying both numbers in the ratio by the amount you are increasing, in this case three. So, to triple our gift basket, we would multiply our 10 by three and our 12 by three to get 30:36 (apples:oranges). We can do this because we remember from algebra that multiplying a mathematical expression by the same number on both sides keeps the expression the same. We can check to see if our ratios are the same by dividing each of them: 10 / 12 = 0.833 and 30 / 36 = 0.833, which are equal. Because they are equal, it tells us that they are proportional.
Lesson Summary
What did we learn? We learned that ratios are value comparisons, and proportions are equal ratios. Ratios can be written with colons or as fractions. So, to compare the number of girls to boys in a litter of puppies, we can write 2:4 or 2/4 to say that there are two girls to four boys. If we double the litter size but the number of girls to boys changes to 4:8, we can say that both litters are in proportion since both ratios divide into the same number. And as we saw, ratios and proportions are used every day by cooks and business people, to name just a few.