Ratio and Proportion Example

This illustrated example shows the link between ratios and fractions. There are four ratios depicted with the use of coloured balls and the fraction of each colour.

Understanding Ratio and Proportion: A Complete Guide with Examples

Ratios and Proportions- both of these are two basic number concepts in maths. In depth understanding of these two core concepts will help your students compare quantities and understand relationships between different values. These concepts are important for the KS2 and KS3 curriculum. You can either be a student learning ratio example or a teacher teaching number skills, this is a perfect resource. Therefore, this guide will help you master the topic.

What is a Ratio?

The basic idea of ratio can easily be explained as a way of comparing two or more different quantities. These calculations tell us how much of one value exists in relation to another value. Let’s take an example-

Example:

Imagine a bag contains 2 red balls and 3 green balls, the ratio of red to green will be 2:3. To explain this a bit more easily, this means for every 2 red balls, there are 3 green balls.

Key Points About Ratios:

1. We can write Ratios in different forms. Here are the different forms that we can use-

• Using a colon → 2:3
• As a fraction → 2/3
• In words → “2 to 3“

2. Ratios can be either scaled up or down, for example-

• 4:6 is equivalent to 2:3 (dividing both by 2).

3. Order matters:

• 2:3 is not the same as 3:2.

What is Proportion?

On the other hand, the concept of proportion shows that two ratios are equal. This idea will help your students find missing values when comparing ratios.

Example:

If the ratio of boys to girls in a class is 3:2, and there are 12 boys, how many girls are there?

1. Set up the proportion:
   32=12x\frac{3}{2} = \frac{12}{x}23​=x12​
2. Solve for xxx (cross multiply):
   3x=12×23x = 12 \times 23x=12×2 3x=243x = 243x=24
3. Divide by 3:
   x=8x = 8x=8

Hence, there are 8 girls in the class.

Ratio Examples

Example 1: Simplifying Ratios

Simplify 12:18.

1. Find the highest common factor (HCF) of 12 and 18 (6).
2. Divide both by 6: 12:18=(12÷6):(18÷6)=2:312:18 = (12 ÷ 6):(18 ÷ 6) = 2:312:18=(12÷6):(18÷6)=2:3

Hence, the simplified ratio is 2:3.

Example 2: Sharing in a Given Ratio

James and Sarah share £50 in a 3:2 ratio. How much does each person get?

1. Find the total number of parts:
   3+2=53 + 2 = 53+2=5
2. Divide £50 into 5 parts:
   50÷5=1050 ÷ 5 = 1050÷5=10
3. Multiply by each ratio part:
    
   • James: 3 × 10 = £30
   • Sarah: 2 × 10 = £20

Hence, James gets £30, Sarah gets £20.

Example 3: Ratios in Real Life

Ratios are used in everyday situations. Here are some mention-worthy examples of using ratios in real life:

• Cooking: A recipe may say 2:1 flour to sugar.
• Maps: A scale of 1:1000 means 1 cm on the map is 1000 cm in real life.
• Business: Profit-to-cost ratios help track earnings.

How to Convert Ratios to Fractions

A ratio can easily be written as a fraction by dividing each part by the total. Let’s take an example-

Example: A class has 4 boys and 6 girls (ratio 4:6). What fraction of the class is boys?

1. Find the total:
   4+6=104 + 6 = 104+6=10
2. Write as a fraction:
   410=25\frac{4}{10} = \frac{2}{5}104​=52​

Hence, 2/5 of the class are boys.