Ratio 1 (AQA GCSE Maths): Revision Notes
Ratio 1
What is a ratio?
Ratios are mathematical tools used to compare quantities. They show the relationship between two or more amounts by expressing how many times bigger one quantity is compared to another.
When you see fruits arranged as 3 apples and 2 oranges, you can express this relationship as a ratio.
Ratios are everywhere in everyday life! You might use them when cooking (2 cups flour to 1 cup water), in sports (goals for and against), or when describing mixtures (paint colours, concrete ingredients).
Writing ratios
You can write ratios in several ways:
- Ratio notation: 3:2 (read as "3 to 2")
- Fraction form: 2/5 of the pieces of fruit are oranges
- Word form: "3 apples to 2 oranges"
Understanding the denominator: The denominator in the fraction form represents the sum of all parts in the ratio. In this example: 3 + 2 = 5, so 2/5 of the fruit are oranges.
Equivalent ratios
Equivalent ratios represent the same relationship between quantities, just like equivalent fractions. You create them by multiplying or dividing both parts of the ratio by the same number.
Worked Example: Creating Equivalent Ratios
Starting with the ratio 5:9:
- Multiply both parts by 2: and , so 5:9 becomes 10:18
- Divide both parts by 10: and , so 10:18 becomes 1:1.8
All these ratios (5:9, 10:18, 1:1.8) are equivalent because they represent the same proportional relationship.
Simplest form
A ratio is in its simplest form when both numbers are whole numbers with no common factors other than 1. This means you cannot divide both parts by the same whole number.
Examples:
- Simplest form: 5:1, 10:9, 2:3, 4:7
- Not simplest form: 1:1.5, 2:10, 2:1, 0.9 (these contain decimals or have common factors)
To write a ratio in simplest form, find the equivalent ratio with the smallest possible whole number values. Always check that both numbers cannot be divided by a common factor.
Worked examples
Worked Example 1: Sharing money in a ratio
Jess and Simon buy a computer, paying in the ratio 2:3. Jess pays £194. How much does Simon pay?
Step-by-step solution:
- Find the value of one part:
- Calculate Simon's payment:
- Answer: Simon pays £291
Key insight: The order of people matches the order of numbers in the ratio.
Worked Example 2: Finding ratios from given information
A school has 220 students. 140 are female. Work out the ratio of male to female students in simplest form.
Step-by-step solution:
- Find number of male students:
- Write the ratio: male = 80:140
- Simplify by dividing both by 20: and
- Answer: 4:7
Practice questions
Test your understanding with these problems:
Practice Problems
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A bag contains white and pink marshmallows in the ratio 3:4. What fraction of the marshmallows are pink?
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Write the ratio 84:120 in its simplest form.
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A bag contains red and green counters in the ratio 4:3. There are 32 red counters. What is the total number of counters?
Remember!
Key Points to Remember:
- Ratios compare quantities and show proportional relationships
- Order matters - 3:2 is different from 2:3
- Equivalent ratios are found by multiplying or dividing both parts by the same number
- Simplest form uses the smallest possible whole numbers with no common factors
- Always check your working and ensure your final ratio makes sense in the context