Rate, Ratio, and Proportional Reasoning Review

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 that 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 by using 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 100, so the denominator of the percent ratio will always be 100.

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