# Ratios

## Lesson Preview

### What You'll Learn

1. To write ratios
2. To find equal ratios

### … And Why

To compare weights, as in Example 4

## Writing Ratios

### Investigation:A Survey of Birthday Data

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1. Take a survey of your class. Find each person's birth month, as in the example at the right.
2. For each month, write the following fraction:
3. 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 .

### Ratio

A ratio is a comparison of two quantities by division. You can write a ratio in three ways.

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.

Ratios

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#### 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

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