A ratio is a comparison of quantities. For example, for most mammals, the ratio of legs to noses is but for humans, the ratio of legs to noses is
Ratios can be written using the word "to," a colon, or a fraction.
For example, in a group of 3 girls and 5 boys, the ratio of girls to boys can be written as or
A bowl contains 3 apples, 5 oranges, and 9 kiwi. What is the ratio of kiwi to apples?
There are 9 kiwi and 3 apples, so the ratio of kiwi to apples is or in simplified form,
A bowl contains 3 apples, 5 oranges, and 9 kiwi. What is the ratio of oranges to total pieces of fruit?
There are 5 oranges and total pieces of fruit, so the ratio of oranges to total pieces of fruit is
Ratios are often easiest to use if written in fraction form. To find an unknown value in a ratio, we can use two equivalent ratios.
For example, if the ratio is equivalent to the ratio then and because the values in the fraction on the right are six times greater than the corresponding values in the fraction on the left.
If what is
Expressing the ratios as fractions, we get
The fraction simplifies to so now we have The values in the ratio on the right are five times greater than the values in the ratio on the left, so
We can also rewrite the ratios as fractions and cross multiply to solve.
If Calvin paid $5 for 7 pencils, how much would he pay for 56 pencils?
Let be the price of pencils. Since the price of a single pencil does not change, we have Hence, Calvin would pay for pencils.
The ratio of Alice's pay to Bob's pay is . The ratio of Bob's pay to Charlie's pay is . If Alice is paid $75, how much is Charlie paid?
Since the ratio of Alice's pay to Bob's pay is , Bob's pay must be , where . Cross-multiplying by the denominators, we get , so .
Continuing in the same way, we compare Bob to Charlie: Thus, Charlie is paid $54.