What are proportions?
Proportions are a fundamental concept in mathematics that help us compare the relative sizes or quantities of two or more things.
Before we dive into proportions, it's important to understand ratios. A ratio is a comparison of two quantities. It's typically written in one of three ways:
As a fraction: For example, the ratio of apples to oranges can be written as "3/2," which means there are 3 apples for every 2 oranges.
Using a colon: The same ratio of apples to oranges can be written as "3:2."
Using the word "to": You can also express it as "3 to 2."
A proportion is essentially an equation that states that two ratios are equal. In other words, if you have two sets of numbers in a proportion, the cross products of those ratios are equal.
The basic proportion formula
The simplest form of a proportion looks like this:
In this equation, a and d are called the extremes, while b and c called the means. The key idea here is that the product of the extremes (a×d) is equal to the product of the means (b×c).
To solve a proportion, you can use the basic proportion formula and cross-multiply. Here are the steps:
Cross-multiply: Multiply the values diagonally across the equal sign.
a × d and b × c.
Solve for the missing value by isolating it on one side of the equation.
For example, if you're trying to find a, divide both sides by d.
Let's say you have a proportion: 2 / 3 = a / 6
To solve for a, you would cross-multiply: 2 × 6 = 3 × a.
Then, simplify: 12 = 3 x a
Finally, isolate a by dividing both sides by 3:
That's the basic idea of simple proportions in math. They are incredibly useful for solving problems involving ratios and comparing quantities in real-world scenarios.
To help students practice proportions in math, we’ve created several worksheets covering simple proportions as well as proportions word problems.
Simple proportions worksheets
In our grade 6 math worksheets section we have a set of worksheets for students to practice simple proportions.
Practice proportions word problems
To think about real-world scenarios, we have also created word problems worksheets for practicing proportions.