Rule of Three or Cross-multiplication

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The rule of three is a simple way to find an answer when you know two parts of a problem.

Imagine you want to make cookies, and the recipe says you need 3 cups of sugar for every 6 cookies. If you want to make 12 cookies, how much sugar do you need?

The rule of three helps you solve this problem by finding the relationship between the two parts of the problem: sugar and cookies. You know that 3 cups of sugar is needed for 6 cookies, so you can use this information to find how much sugar you need for 12 cookies.

To do this, you can multiply both parts of the original relationship (3 cups and 6 cookies) by the same number to keep the relationship the same. In this case, you could multiply both parts by 2, so now you have 6 cups of sugar and 12 cookies. This means you now have the answer, which is 6 cups of sugar!

The rule of three is a simple and easy way to solve problems that have a relationship between two parts.

The rule of three is a mathematical method used to solve problems related to ratios and proportions. It is based on the idea that if two quantities are in proportion, then a mathematical relationship can be established between them.

For example, if we know that A is in relation to B in a proportion of 2:5, and we want to know what the value of B is if A is 10, we can use the rule of three to find the answer.

AB=25\dfrac{A}{B} = \dfrac{2}{5}

The rule of three is usually done using a table with three columns, where we place the known quantity, the unknown quantity, and the coefficient.

AB2510x\dfrac{A}{B} \quad \dfrac{2}{5} \quad \dfrac{10}{x}

For the example above, we would have:

25=10x\dfrac{2}{5} = \dfrac{10}{x}

By multiplying the known value by the inverse coefficient, that is 5/25/2, we get the unknown value:

x=1052=25x = \dfrac{10*5}{2} = 25

The rule of three is often used to solve problems related to unit conversion, percentages, interests, among others.

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