Find the fourth proportion to 2, 3, 6

Answer:

A proportion is a statement that two ratios are equal. If four quantities a, b, c, d are in proportion, it means that the ratio of the first two quantities is equal to the ratio of the last two quantities. This is written as a : b :: c : d or a/b = c/d.
In a proportion a : b :: c : d, 'a' is the first term, 'b' is the second term, 'c' is the third term, and 'd' is the fourth proportion.
The key property of a proportion is that the product of the extremes (first and fourth terms) is equal to the product of the means (second and third terms). So, for a : b :: c : d, we have a × d = b × c.

To find the fourth proportion (d) when three numbers (a, b, c) are given, we use the formula derived from the property of proportion: d = (b × c) / a.
Let's apply this to the given numbers: a = 2, b = 3, c = 6.
Using the formula: d = (3 × 6) / 2.
Calculating the product of the means: 3 × 6 = 18.
Dividing by the first term: 18 / 2 = 9.
Therefore, the fourth proportion to 2, 3, 6 is 9. This means 2 : 3 :: 6 : 9, which simplifies to 2/3 = 6/9, confirming the equality of ratios.

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