OCR GCSE Maths: Understanding and Simplifying Ratios

OCR GCSE Maths: Understanding and Simplifying Ratios

What are Ratios?

Ratios are a way to compare two or more quantities. They show how much of one thing there is compared to another. For example, a ratio of 2:1 means that for every two of something, there is one of something else.

Expressing Ratios

Ratios can be expressed in several ways:

• Colon notation: 2:1
• Fraction form: 2/1
• Verbal form: "two to one"

Finding Ratios

To find a ratio, you simply need to express the quantities in their simplest form.

Example:

Let's say there are 12 apples and 6 oranges. To find the ratio of apples to oranges, we simplify the quantities:

• Apples: 12
• Oranges: 6

The ratio of apples to oranges is 12:6, which can be simplified to 2:1.

Simplifying Ratios

Just like fractions, ratios can be simplified by dividing both sides by their highest common factor (HCF).

Example:

The ratio 10:5 can be simplified by dividing both sides by 5:

• 10 ÷ 5 = 2
• 5 ÷ 5 = 1

Therefore, the simplified ratio is 2:1.

Interpreting Ratios in the form 1:n

Sometimes, you'll need to express a ratio in the form 1:n, where n is a number. This means you need to adjust the ratio so that one side is equal to 1.

Example:

The ratio 3:2 can be expressed in the form 1:n by dividing both sides by 3:

• 3 ÷ 3 = 1
• 2 ÷ 3 = 0.66 (rounded to two decimal places)

Therefore, the ratio 3:2 is equivalent to 1:0.66.

Dividing a Quantity in a Ratio

To divide a quantity into a given ratio, you need to find the total number of parts in the ratio and then divide the quantity by that number. Finally, multiply each part of the ratio by the result to find the share of each part.

Example:

Imagine you need to divide £30 into the ratio 2:3.

1. Find the total parts: 2 + 3 = 5
2. Divide the quantity by the total parts: £30 ÷ 5 = £6
3. Multiply each part of the ratio by the result:
4. £6 x 2 = £12
5. £6 x 3 = £18

Therefore, the quantity is divided into £12 and £18.

Remember:

• Ratios are a powerful tool for comparing and understanding relationships between quantities.
• Simplifying ratios makes them easier to understand and work with.
• Understanding how to divide quantities in a given ratio is essential for solving many practical problems.