Extended proportion is a concept in mathematics that refers to a series of equal ratios or fractions, where the terms are in proportion to one another. An extended proportion arises when you have more than two ratios, and they're all equal.
In an extended proportion, the product of the extreme terms (the first and the last) is equal to the product of the mean terms (the rest of them in between).
For example, consider the extended proportion a:b = c:d = e:f where a, b, c, d, e, and f are numbers.
To demonstrate this concept with an example, let's take the following extended proportion:
2:4 = 3:6 = 4:8
In this example, the ratios are:
2/4 = 3/6 = 4/8
Since all of the ratios are equal (1/2), this is an extended proportion. The product of the extreme terms (2 × 8 = 16) is equal to the product of the mean terms (4 × 3 × 4 = 48; 48 ÷ 3 = 16).
Extended Proportion
Definition and Example
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