Proportion
When two values of a quantity are compared to each other, it is a ratio of values. For example, comparing the weight of loads as 150 kg and 50 kg, then the ratio will be
In this case, it is said that load 1 is 3 times heavier than load 2.
Proportions are equations, both sides of which are ratios. Familiar examples of using a comparison are scale (drawing, map, etc.) and roof slope.
Motivation
Consider a cooking situation, where the recipe has the following instructions for us: for 2,5 cups of flour, add 2 tablespoons of oil. If we added 10 cups of flour, how much oil would we need?
This problem is a typical example of a proportion equation. In the equation, we have two quantities, where the proportion (ratio) of the quantities is known. If the amount of one of the quantities is known, we can solve the amount of the other quantity. The unknown quantity is denoted by x and it is solved from the equation.
You can start by making a table:
Proportion is easily done by writing the columns as fractions:
| flour | oil | |
| 2,5 cups | 2 Tbsp | |
| 10 cups | x | |
Algorithm
Simple proportion equations have an algorithm that can be used for
obtaining the solution of the equation:
1. Cross multiplication: multiply the numerator of the first ratio with
the denominator of the second ratio, and also multiply the denominator
of the first ratio with the numerator of the second ratio. Both products
yield the same value, creating a new equation that is equivalent to the
original equation.
2. Divide the equation by the coefficient of the unknown variable.