Ratio 1 (Edexcel GCSE Maths): Revision Notes
Ratio 1
What are ratios?
Ratios are mathematical tools that allow us to compare different quantities or amounts. When you want to show the relationship between two or more values, ratios provide a clear way to express this comparison.
For example, if you have 3 apples and 2 oranges, you can express this relationship as a ratio. The ratio of apples to oranges would be written as 3 : 2.
The colon (:) is the standard symbol used to separate the quantities being compared in a ratio. Think of it as meaning "to" - so 3:2 reads as "3 to 2".
Writing ratios from quantities
To write a ratio, you simply count the quantities you want to compare and write them in order, separated by colons (:).
The process involves these key steps:
- Count the first quantity
- Count the second quantity
- Write as first quantity : second quantity
The ratio 3 : 2 is already in its simplest form because 3 and 2 cannot be divided by any common number other than 1.
Converting ratios to fractions
You can express any ratio as a fraction by understanding that the denominator equals the sum of all parts in the ratio.
For the ratio 3 : 2:
- Total parts =
- Fraction of apples =
- Fraction of oranges =
This means that of all the fruit pieces are oranges, and are apples.
When converting ratios to fractions, always remember that the denominator represents the total of ALL parts in the ratio, not just one part.
Equivalent ratios
Equivalent ratios represent the same relationship but use different numbers. You can create equivalent ratios by multiplying or dividing both parts by the same number.
Starting with 5 : 9:
- Multiply both by 2: 10 : 18
- Divide both by 10: 1 : 1.8
The form 1 : 1.8 is particularly useful for calculations because it shows how many units of the second quantity correspond to 1 unit of the first.
The form where the first number is 1 (like 1 : 1.8) is called the "unitary form" and is especially helpful for scaling calculations.
Simplest form
To write a ratio in its simplest form, you need to find an equivalent ratio using the smallest possible whole numbers.
Examples of Simplest Form:
Correct simplest forms:
- 5 : 1 ✓
- 10 : 9 ✓
- 2 : 3 : 4 ✓
Incorrect forms (not in simplest form):
- 1 : 1.5 : 2 ✗ (contains decimals)
- 10 : 2 ✗ (can be simplified to 5 : 1)
- 1 : 0.9 ✗ (contains decimals)
To simplify a ratio, find the highest common factor of all parts and divide each part by this number.
Simplest form ratios should only contain whole numbers, and these numbers should have no common factors other than 1.
Problem solving with ratios
Money sharing problems
When people share money in a given ratio, follow these essential steps:
- Find the total ratio parts by adding all numbers in the ratio
- Calculate the value of one part by dividing the total amount by the total parts
- Multiply each person's ratio part by the value of one part
Worked Example: Money Sharing
Jess and Simon share costs in the ratio 2 : 3. If Jess pays £194, how much does Simon pay?
Step 1: Identify what we know
- Jess pays 2 parts of the ratio
- Jess pays £194
Step 2: Find the value of one part
- Jess pays 2 parts = £194
- One part = £194 ÷ 2 = £97
Step 3: Calculate Simon's payment
- Simon pays 3 parts
- Simon pays 3 × £97 = £291
Finding ratios from given information
When you know the quantities, work backwards to find the ratio by calculating each quantity first, then writing the ratio.
Worked Example: Finding Ratios
A school has 200 students, 120 are female. Find the ratio of male to female students.
Step 1: Calculate missing quantity
- Male students = 200 - 120 = 80
Step 2: Write the ratio
- Ratio = male : female = 80 : 120
Step 3: Simplify
- Divide both by 40: 2 : 3
Always read the question carefully to ensure you write the ratio in the correct order - "male to female" means male : female, not female : male.
Exam tips
Essential Exam Strategies:
- Always check if your final answer needs to be in simplest form
- Show your working clearly, especially when finding equivalent ratios
- Remember that the order matters in ratios - make sure you write them in the correct sequence
- When sharing amounts, always verify your answer by checking the parts add up to the total
Key Points to Remember:
- Ratios compare quantities using the format first : second
- Equivalent ratios can be found by multiplying or dividing both parts by the same number
- Simplest form uses the smallest possible whole numbers
- When converting to fractions, the denominator equals the sum of all ratio parts
- For problem solving, find the value of one part first, then multiply to find individual amounts