# Ratios

## Lesson Preview

## What You'll Learn- To write ratios
- To find equal ratios
## … And WhyTo compare weights, as in Example 4 |

## Writing Ratios

### Investigation:A Survey of Birthday Data

- Take a survey of your class. Find each person's birth month, as in the example at the right.
- For each month, write the following fraction:
- If there are the same number of birthdays in each month, each fraction will equal . Find whether each of your fractions is greater than, less than, or equal to .

In a middle school class, 5 of the 24 students were born in August. You can compare the numbers 5 and 24 by dividing to form the ratio .

Look at the photograph. The keys of a piano have a repeating pattern of five black keys and seven white keys. You can use ratios to describe the pattern.

You can use a ratio to compare part to part. The ratio of black piano keys to white piano keys in the pattern is 5 : 7. You can also compare part to whole. The ratio of black keys to all keys in the pattern is 5 : 12.

#### Writing Ratios

MusicUsing the pattern shown above, write the ratio of black keys to all keys in three ways.

You can use decimals to express and compare ratios.

#### Writing Ratios as Decimals

Social StudiesAn official U.S. flag has a length-to-width ratio of 19 : 10. The largest U.S. flag measures 505 ft by 255 ft. Is this an official U.S. flag?

Since 1.98 is not equal to 1.9, the largest flag is *not* an official United States flag.

Interactivity Understanding ratios