Ratio and Proportion – GCSE Maths

Introduction

When we compare two quantities or numbers using division, then it is called Ratio and Whenever we compare ratios , then it is called Proportion.
In the following example we are equating two ratios and it is called Proportion.

Ratios and Proportions

Ratios allows us to compare two quantities by showing how much of one quantity is contained by the other.
Proportions on the other hand tells us that the ratios are equal. There can be two or more ratios in proportion to each other.

$Diagram comparing ratios 5:10 and 2:4 using shaded fractions of shapes to explain proportional equivalence$

Solved Example

Problem: Find the ratio of the shaded portion to unshaded for both the diagrams check whether they are in proportion or not?

Solution:

In the first box 50 out of 100 boxes are shaded. Therefore, the ratio:

In the second box 18 out of 36 boxes are shaded, thus the ratio:

We can clearly see that both the ratios are equal thus they are in proportion, so can be represented by:

Final Answer: 50 : 100 : : 18 : 36

Solved Example

Problem: Find out the ratios of blue balls and green balls differently and also check if they are in proportion or not?

Solution:

In the first row the total blue balls are 3 and green balls are also 3. In the 2nd row there is single blue ball with 2 green balls:

$One purple counter and two green counters with a fraction 1/2 shown beside to illustrate the ratio visually$

In the 3rd row there are 2 blue balls and 3 green balls:

$Two purple counters and three green counters beside fraction 2/3 showing a 2:3 ratio visually$

In the 4th row there are 3 blue and 2 green balls. ratio:

$Three purple counters and two green counters with fraction 3 over 2 shown to represent ratio 3:2$

We can conclude the ratios do not represent a common ratio, hence they are not in proportion.

Solved Example

Problem: Suppose in a school there are total 130 students in which there are 50 girls and 80 boys. If one day 25 out of 50 girls and 40 out of 80 boys were present that day then check whether these ratios (present girls and boys to the total ) are in proportion or not?

Solution:

Total = 130, Girls = 50, Girls present = 25, Boys = 80, Boys present = 40

Ratio of the present girls to the total no. of girls :

$Ratio 25 to 50 shown with fraction 25/50 simplified to 1/2 to represent an equivalent proportion$

Ratio of the present boys to the total no. of boys:

$Ratio 40 to 80 shown as 40/80 equals 1/2 to illustrate equivalent ratios in fraction form$

Both the ratios are equivalent, thus they are in proportion so we can write them as:

Final Answer: 25 : 50 :: 40 : 80

Solved Example

Problem: If there are four friends A, B, C and D. A and B have a total of £50, they share it so that A got £20 and B got £30. Similarly C and d share the total amount of £100 such that C got £40 and D got £60. Find the ratios of sharing and compare them that they are in proportion or not?

Solution:

They distribution of 50 in A and B:

A = 20 , B = 30

Ratio:

They distribution of 100 in A and B:

A = 40 , B = 60

Ratio:

$Simplified ratio of 40 to 60 shown as 2 to 3 using fraction method$

Final Answer: The ratios are equal and are in proportion

Solved Example

Problem: Olivia is going to make some ice cream. She needs to mix Custard powder, Milk and sugar in the ratio – 1 : 4 : 20 If she has 25g of Custard 100g of Sugar 500g of Milk Does Olivia has enough Custard, Sugar and Milk to make ice cream?