Ratios & Proportions Examples

At a local bookstore, for every 100 books sold, 68 of them are fiction. What is the ratio of nonfiction books to total books sold?

Since 68 books of every 100 sold are fiction, it's a safe bet that the remaining books are nonfiction. That means there are 100 – 68 = 32 nonfiction books for every 100 sold. Ratios are usually written as fractions, so:

We can reduce this by dividing by 4.

James has quite a bit of free time each day. He often spends 4 hours on the computer and the other 2 hours playing basketball. What is his ratio of basketball to computer time? What ratio of his total free time is spent on basketball?

To answer the first question, compare the number of basketball hours (2) to the number of computer hours (4).

That’s 2:4. This ratio can be reduced to 1:2, by dividing each by 2.

For the second question, compare James' hooping hours (2) to his total free time (2 + 4 = 6). We can write this ratio as a fraction:

Then reduce it to  by dividing the numerator and denominator by 2.

The ratio of frogs to tadpoles in a pond is 3:4. After scooping up some frogs and tadpoles in a jar, our ratio of frogs to tadpoles is 9:13. Is the ratio of amphibians in our jar proportional to the ratio of amphibians in the entire pond?

We first write a ratio for the amphibians in the pond and then one for the amphibians in our jar.

Pond ratio:
Jar Ratio:

Then we test to see if the ratios are equal to each other. If they are, they form a proportion. If not, they don't.

We can write an equivalent fraction to by multiplying the top and bottom by 3. That gives us . And while is close to , it isn't equal, so these do not form a proportion.

The ratio of glass beads to metal beads on a bracelet is 4:5, and the ratio of these beads on a necklace is 28:35. Do the bracelet and necklace have a proportional number of beads?

The ratio of beads on the bracelet is .

The ratio of beads on the necklace is .

Do these form a proportion?

Because we can divide both 28 and 35 by 7, we can simplify the second ratio to . Now we have . Yep, they're proportional.