## Understanding ratios: GCSE curriculum

**A ratio is a way to compare two or more quantities, showing how many times one quantity is larger or smaller than another**. It is important for decision-making and problem-solving because it provides a way to quantify relationships and making meaningful comparisons.

**As a fraction**: If there are 4 bananas and 8 apples, we can write the ratio of bananas to apples as 1/2. This means there are two times as many apples compared to bananas.**With a colon**: Using the same fruit example, this ratio can also be expressed as 1:2.**Using the word 'to'**: You could also see this comparison written as "1 to 2". This is the least common way to express a ratio.

### Types of ratios

**Part-to-part**: This ratio compares different parts of a group to each other, like the apples to oranges above. Both of these items are in the same group of fruit.**Part-to-whole**: This compares one part of the group to the entire group. In the fruit example, there are 12 pieces of fruit (4 bananas and 8 apples). There are 4 bananas with a part-to-whole ratio for all the fruit of 4:12. This simplifies to 1:3.**Rates**: A rate is a unique ratio where the quantities being compared have different units. Taking the fruit example further, this could be carbohydrates or calories for bananas and apples.

### 1

You're preparing a fruit salad that needs a ratio of apples to oranges of 2:3. If you already have 6 apples, how many oranges do you need?

## Calculate a ratio

**Example:**

- Length of the model - To find the model length, we need to divide the actual length by the scale factor. This is 500 / 100 = 5 meters
- Width of the model = To find the model width, we need to divide the actual width by the scale factor. This is 40 / 100 = 0.4 meters

### Simplifying ratios

- Find the GCD: Look for the highest number that divides both parts of the ratio, keeping each part a whole decimal without a remainder.
- Divide: Divide each part of the ratio by the GCD that you have found.

**Example:**

### 2

You need to landscape a garden and want a ratio of flowering plants to green plants of 3:2. If there are 45 flowering plants, how many green plants do you need?

## Use ratios in problem-solving

**Recipes**: You can change the quantity of each ingredient to make a larger or smaller dish while keeping the taste and texture the same.**Chemistry**: To create the desired chemical reaction, you need to mix chemicals with precise ratios to avoid wastage or dangerous outcomes.**Finance**: Ratios are used to analyse financial statements. For example, a ratio called "debt-to-equity" is used to discover the balance between money borrowed by a business and the funds owned by shareholders.

**Example:**

- The ratio is 3 parts grass and 1 part paved. This means a total of 4 parts.
- Each part is the total (16,000) divided by 4 = 4,000 square meters.
- This means that the paved area (1 part) will be 4,000 square meters.

### 3

In a classroom, the ratio of students to computers is 3:1. If there are 36 students in the class, how many computers are needed?

## Common mistakes and tips

### Tips for success

**Practice regularly**: Irritating as it may sound, practice really does make perfect. Work through from basic to increasingly complex ratios to increase your understanding and confidence.**Visualise the problem**: Draw a diagram or even use a physical object to help you see the relationship shown by the ratio. It's an especially useful technique when you're dealing with complex scenarios.**Check your work**: Always double-check your calculations and the logic of your ratios. It's a good idea to invert the operation and see if you return to the original quantities.

### 4

You need to mix paint to create a custom colour. The ratio of red to blue paint is 3:2. If you start with 6 litres of red paint, how many litres of blue paint do you need?

## Ratios in advanced applications

**Statistics**

**Engineering**

- The Gear ratios in machines determine the speed and torque of moving parts, which are essential for designing efficient mechanical systems.
- Aspect ratios are used in civil engineering to influence the stability and aesthetics of buildings.

**Economics**

### Applying advanced ratios

### 5

An investor analyses two companies; Company A has a price-to-earnings ratio of 25, while Company B has a ratio of 15. If all other factors are equal, which company's stock represents a better value for money?

## Conclusion

## Frequently asked questions

## Glossary

- Ratio - A comparison of 2+ quantities, showing how many times one value is greater/smaller than the other.
- Proportion - An equation that states two ratios are equal. It helps for solving problems where one part of the ratio is unknown.
- Rate - A specific kind of ratio where the quantities have different units, like speed (miles per hour) or density (people per square mile).
- Scale

- The ratio of the dimensions of a model to the dimensions of the original. This is often used in drawings, models and maps. - Scale factor - A number which scales or multiplies some quantity. It is used to adjust the sizes or amounts in direct proportion to the factor.
- Direct proportion - When two quantities increase or decrease at the same rate. This means their ratio remains constant.
- Inverse proportion - A relationship where one quantity increases as another decreases.
- Simplify - Reducing a ratio to its smallest form by dividing both terms by their greatest common divisor.
- Part-to-part - A comparison between two distinct groups in a larger set, focusing on the relationship between these two groups alone.
- Part-to-whole - A comparison where one part is compared to the total, combining all parts into a total.

*This post was updated on 30 Nov, -0001.*