A **rate** is a ratio. A **ratio** is a comparison of two numbers. A ratio can be expressed three ways:

- Using the fraction bar as in 2/3.
- Using a colon symbol as in 2:3.
- Using the word “to” as in 2 to 3.

When the denominator of a rate is 1, we call the rate a **unit rate**. We usually use the key word “per” or the division symbol ( / ) to indicate a unit rate. A ratio table is another way of finding answers to ratio problems. With a ratio table, you start with a known ratio and use it to find other numbers with the same ratio. You can keep using the numbers you find to discover more numbers until you solve the problem.

A **proportion** is an equation which states that two ratios are equal. To solve a proportion, you simply cross multiply to find the missing value. There are three parts to every proportion: 2 fractions and an equal sign. Each of the fractions by itself is a ratio. The numerator of the first ratio and the denominator of the second ratio are called the **extremes**. The denominator of the first ratio and the numerator of the second ratio are called the **means**.

We can designate equivalent amounts of a whole by using a fraction, a decimal number, or a percent. To change a fraction to a decimal, divide the numerator by the denominator. To change a decimal to a percent, we move the decimal point two places to the right. To change a percent to a decimal, move the decimal two places to the left. Remember, percent means out of (per) 100, so the denominator of the percent ratio will always be 100.

## Practice

1) Write the ratio in another form. 9:6

2) Write the ratio of ones to zeros. 1110000

3) There are 145 students in your school chorus program. 25 students sing soprano and 15 sing alto. Write a ratio of the number of altos to all the students in the chorus program. Write your answer in lowest terms.

4) Make the ratios equal. 9/25 = 36/?

5) The ratio of apples to oranges in a fruit bowl is 1 to 4. If there are 8 apples in the bowl, how many oranges are there?

6) 2 pounds of apples cost $0.76. How much would 5.5 pounds cost?

7) If it is $55 for 20 people, how much for one?

8) Which is the better deal: 5 cans of soda for $2.27 or 7 cans of soda for $2.89?

9) Which is traveling faster? Traveling 350 miles in 5 hours or traveling 215 miles in 3 hours?

10) Which is traveling faster? Traveling 170 yards in 45 seconds or traveling 416 feet in 35 seconds

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