Ratio
Definition

A ratio is a comparison of numbers or quantities.

A ratio of two numbers can be written as a fraction (or simplified as a decimal), but may not represent the same thing a fraction does. The denominator of a fraction ALWAYS represents the number of equal parts a whole is divided into.

A ratio can compare numbers with the same or different units.

Demonstration Image only

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Example One (A Three Term Ratio)

The illustration below shows a set of marbles. There are two red marbles, six green marbles and four blue marbles in the set. The ratio of red marbles to green marbles to blue marbles could be expressed in the following ways:

• 2 to 6 to 4
• 2:6:4

Note that the ratio 1 to 3 to 4 is said to be equivalent to the ratio 2 to 6 to 4, that is 2:6:4 = 1:3:2.

Example Two (A Two Term Ratio)

The illustration below shows a set of marbles. There are two red marbles and four blue marbles in the set. The ratio of red marbles to the total number of marbles could be expressed in the following ways:

• 2 to 6
• 2:6
• Note that the ratio 2 to 6 is said to be equivalent to the ratio 1 to 3, that is 2:6 = 1:3.

Note also that a fraction is a number that stands for "part of something". This ratio expresses the part of the set of marbles that are red.

Example Three (A Two Term Ratio)

The illustration below shows a set of marbles. There are two red marbles and four blue marbles in the set. The ratio of red marbles to blue marbles could be expressed in the following ways:

• 2 to 4
• 2:4
• • 0.5

Note that the ratio 2 to 4 is said to be equivalent to the ratio 1 to 2, that is 2:4 = 1:2.

Note also that a fraction is a number that stands for "part of something", so although this ratio can be expressed as a fraction, in this case it does NOT represent "part of something".

Example Four (A Two Term Ratio)

The illustration below shows three plates, each with four slices of pizza. The ratio of slices of pizza to plates could be expressed in the following ways:

• 12 to 3
• 12:3
• • 4

Note that the ratio 12 to 3 is said to be equivalent to the ratio 4 to 1, that is 12:3 = 4:1.

Note also that a fraction is a number that stands for "part of something", so although this ratio can be expressed as a fraction, in this case it does NOT represent "part of something".

Note also that ratios can have units in each part of a ratio. Here the ratio represents the number of slices of pizza to the number of plates.