EDEXCEL GCSE FOUNDATION MATHS - What are Ratio

Edexcel GCSE Foundation Maths - What are Ratios?

What is a Ratio?

A ratio is a way of comparing two or more quantities. It shows how much of one quantity there is compared to another. We use the symbol ':' to separate the quantities.

Example:

Imagine a bag of sweets containing 5 red sweets and 3 blue sweets. The ratio of red sweets to blue sweets is 5:3. This means for every 5 red sweets, there are 3 blue sweets.

Understanding Ratios:

1. Order Matters: The order of the quantities in a ratio is important. 5:3 is different from 3:5.
2. Simplifying Ratios: You can simplify ratios just like fractions. To do this, find the highest common factor (HCF) of the numbers in the ratio and divide both sides by it.
3. Parts: The numbers in a ratio represent 'parts' of a whole. In the example above, the ratio 5:3 represents 8 parts in total.

Writing Ratios:

• From Words to Ratios: Convert words into ratios by identifying the quantities and their order.
• From Fractions to Ratios: A fraction can be written as a ratio by putting the numerator and denominator on either side of the colon.

Using Ratios to Solve Problems:

1. Finding a Quantity: If you know the total quantity and the ratio, you can work out the individual quantities.
2. Scaling Ratios: If you know a ratio and want to increase or decrease the quantities, you need to multiply or divide both parts of the ratio by the same factor.

Examples:

Example 1: Simplifying Ratios

Simplify the ratio 12:18

• Find the HCF: The highest common factor of 12 and 18 is 6.
• Divide both sides: 12 ÷ 6 = 2 and 18 ÷ 6 = 3
• Simplified Ratio: The simplified ratio is 2:3

Example 2: Finding a Quantity

A recipe for cake calls for flour and sugar in the ratio 3:2. If you use 600g of flour, how much sugar do you need?

• Calculate total parts: 3 + 2 = 5 parts
• Find the value of one part: 600g ÷ 3 = 200g
• Calculate sugar: 2 parts x 200g = 400g
• Answer: You need 400g of sugar.

Example 3: Scaling Ratios

The ratio of boys to girls in a class is 2:1. If there are 14 boys, how many girls are there?

• Determine the scaling factor: 14 ÷ 2 = 7 (This means each 'part' in the ratio represents 7 students)
• Apply the scaling factor to girls: 1 x 7 = 7
• Answer: There are 7 girls in the class.

Practice and Application:

Practice solving ratio problems using different scenarios and examples. Ratios are used in many real-life applications, such as cooking, mixing ingredients, sharing money, and comparing sizes.