Demystifying Ratios: A Simple Step-by-Step Guide
Mathematics can be an exciting adventure if you approach it with the right tools and mindset. In this blog, we will delve into the concept of ratios, a fundamental topic in mathematics. Whether you are a student just beginning to study maths or simply seeking a refresher, this comprehensive guide will help you understand and apply ratios effectively. With clear explanations, practical examples, and a test yourself section, you’ll gain the confidence you need to tackle ratios with ease.
What is a Ratio?
A ratio is a way of comparing two or more quantities. It shows the relationship between these quantities using numbers or symbols. Ratios are used in everyday life, such as in cooking, mixing substances, or comparing measurements.
Let’s break down the key components of ratios in a step-by-step manner:
Step 1: Identifying the Parts
In a ratio, there are two or more quantities being compared. These quantities are called terms. For example, if we have a ratio comparing apples to oranges, the terms are “apples” and “oranges.”
Step 2: Expressing Ratios
Ratios can be represented in different ways, depending on the context. The most common ways to express a ratio are using the colon (:) or the word “to.” For instance, if we have a ratio of 2:5 comparing apples to oranges, it can be written as “2:5” or “2 to 5.”
Step 3: Simplifying Ratios
Sometimes, ratios can be simplified to their simplest form. To simplify a ratio, find a common factor that divides both terms evenly. Divide each term by this factor until you can no longer simplify.
For example, if we have a ratio of 4:8, we can simplify it by dividing both terms by 4 to get 1:2.
Using Ratios: Examples and Applications
Example 1: Scaling Ratios
Ratios can help us scale quantities up or down. Suppose you have a recipe that serves 4 people, but you need to adjust it to serve 8. If the original ratio of ingredients is 2:1 (flour to sugar), you can double the quantity of both ingredients by multiplying each term by 2. Thus, the new ratio becomes 4:2.
Example 2: Solving Problems
Ratios are powerful tools for problem-solving. Let’s consider a problem that states, “For every 3 boys, there are 5 girls in a class.” If the class has 9 boys, how many girls are there?
There are two ways that we can approach this problem.
Attempt 1
To answer this question we need to write out the ratio we are working with, which is 3:5
We know that there are 9 boys in the class and we know that the ratio of boys is 3
To find out the proportion of boys in the class we divide the 9 by its ratio: 9 ÷ 3 = 3
We take that 3 and multiply it by the 5 in our ratio: 5 x 3 = 15
Therefore, there are 15 girls in the class.
Attempt 2
Set up a proportion by writing the ratio as 3:5 and cross-multiply 3 × X = 5 × 9.
Solving the equation, we find that X = 15. So, there are 15 girls in the class.
BUT WAIT!
How did we work out that X = 15?
If you look at the equation, we have the sum of 5 x 9 which equals 45.
What we need to do next is find out how many times 3 goes into 45, so we do 45 ÷ 3 which equals 15.
Therefore we now know that X = 15.
Example 3: Comparing Ratios
Ratios allow us to compare quantities in a meaningful way. For example, let’s compare ratios 2:3 and 4:6. To compare ratios, find a common factor that makes both ratios equivalent.
In this case, both ratios can be simplified to 2:3, indicating that they are equal.
Test Yourself
- Simplify the ratio 12:16
- If the ratio of boys to girls in a class is 3:4 and there are 15 boys, how many girls are there?
- Compare the ratios 6:8 and 9:12. Are they equal? Explain your answer.
