Ratio Versus Proportion
Both are used for comparison. Ratios demonstrate a relationship between two numbers; proportions show the equivalence between two ratios.
For example, Liesel is enrolled at Learning Community College. For every 10 students, there are 3 college employees. Therefore, the ratio is 10 to 3.
The proportion would be students and employees as a whole based on the ratio 10 to 3. If there are 1,500 students, then there are 450 employees. In proportion terms, 10:3 = 1,500:450.
Ratios
Ratios can be written as a fraction (⅗), colon separating the two numbers (3:5), and in words (3 apples to 5 oranges).
Liesel has six textbooks this semester. Two of the textbooks are math and the other four are not math-related. What is the ratio of math to non-math textbooks? Write ratio in all three ways.
Proportions
Now let’s compare two ratios to make sure that they are equivalent. In order to do this, set up the two ratios as fractions with the equal sign between them. To check that your proportion is correct, the two sets of cross-multiplied numbers should equal the same number.
At PJ’s Pet Daycare, the ratio of cats to dogs is 3:5. If the total number of pets enrolled is 80, then how many of them are cats?
With a ratio of 3:5, the daycare cares for three cats for every five dogs. Simplified this means that if the daycare only cared for eight animals, you would know that three would be cats and the rest would be five dogs. That is how we get the fraction, ⅜, to work the problem. Multiply that by the total number of pets to suss out how many of the total would be cats.
Sometimes you need to do a little calculating to determine your second ratio. Set up the problem normally, but use x in place of your unknown number. The first fraction will be your known ratio. After setting up your two fractions, cross-multiply to determine what x is. See the question below as an example.
We have a recipe for dog biscuits that requires two cups of flour. This makes 25 dog biscuits. Liesel’s birthday party is next week so we need to make triple the regular amount. How many cups of flour will the recipe need in order to make 75 dog biscuits?
Problems dealing with finding the proportion are pre-algebraic equations so not only did you learn how to find the proportions, you also now have a foundation for algebra!
Other Comparisons
When comparing two numbers, you determine if those numbers are equal to each other or is the first number is greater than or less than the second number. To do this, use symbols = (equal to), > (greater than), < (less than).
Three other symbols that are also useful in math, especially when writing computer programs are: ≠ (not equal to), ≥(greater than or equal to), ≤ less than or equal to). For now, we will just focus on the first three: =, >, <.
If you have trouble remembering which way the symbol should go for greater than or less than, think of the symbol as an open mouth. The open mouth will always face the bigger number. Liesel likes to draw her symbols as Pac-Man, but another popular way is a gator mouth!
