Ratios

Understanding Ratios

• A ratio is a method of comparing or expressing a relationship between two quantities.
• Ratios can be written in different formats: ‘3 to 2’ can also be written as ‘3:2’ or ‘3/2’.
• You must always simplify ratios when possible. For instance, the ratio 4:8 can be simplified to 1:2.

Dividing a Quantity into a Given Ratio

• It is crucial to comprehend how to share a set amount following a certain ratio.
• To divide a quantity in a given ratio, first add the two segments of the ratio to get the total parts, then divide the total quantity by the total parts, then multiply this value by each part of the ratio.
• For example, to share £40 in the ratio 2:3, add 2+3 to get 5 total parts. Then divide £40 by 5 to get £8 per part. Then the shares would be 2x£8 and 3x£8, which is £16 and £24 respectively.

Ratio and Proportions

• Understanding proportion is essential when working with ratios. If two quantities are in the same ratio, they are directly proportional.
• Proportions describe how two quantities change with respect to each other. This is often presented as “directly proportional” or “inversely proportional”.

Applying Ratios to Real-Life Applications

• Ratios are often applied in real-world contexts such as recipes, maps, scale drawings and financial situations. Make sure that you’re comfortable applying your knowledge in these contexts.
• A common requirement in the understanding of ratios is the application to scale drawings. A scale can be seen as a type of ratio. For example, on a map with a scale of 1:50000, one centimetre on the map represents 50000 centimetres (or 500 metres) in real life.

Solving Problems with Ratios

• In questions, you might be given a ratio and one of the total parts, and then asked to find the other part. This involves proportional division.
• Alternatively, you might need to solve a problem involving an increase or decrease in ratio. This requires understanding how ratios remain consistent even as the quantities involved change.