The Importance of Learning about Proportions in Math

What are proportions?

Proportions are a fundamental concept in mathematics that help us compare the relative sizes or quantities of two or more things.

Understanding ratios

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."

Proportions defined

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:

Proportions explained

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).

Proportions explained

Solving proportions

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.

Proportions explained

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.

Proportions explained

Proportions example

Let's say you have a proportion:  2 / 3 = a / 6

Proportions example

To solve for a, you would cross-multiply: 2 × 6 = 3 × a.

Proportions example

Then, simplify: 12 = 3 x a

Finally, isolate a by dividing both sides by 3:

Proportions example

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.

Proportions worksheets

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.

Proportions worksheets

Practice proportions word problems

To think about real-world scenarios, we have also created word problems worksheets for practicing proportions.

Proportions word problems

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