Ratios
A comparison of two quantities by division.
Key idea
A comparison of two quantities by division.
In depth
A ratio compares two quantities by division: a:b means a for every b. Like fractions, ratios can be scaled up or down without changing the relationship. Order matters.
Worked example
A mix has 2 cups of flour to 3 of sugar: 2:3. Doubling gives 4:6.
Formula
Real-world uses
- Mixing paint or concrete
- Comparing team sizes
- Reading scale on maps and recipes such as 2:1 flour to sugar
Common mistake
Reversing the order, or confusing part-to-part (2:3) with part-to-whole (2/5).
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Ratios?
A comparison of two quantities by division. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Ratios?
The key formula is a : b.
Where is Ratios used in real life?
Real-world examples: Mixing paint or concrete; Comparing team sizes; Reading scale on maps and recipes such as 2:1 flour to sugar.
What should I learn before Ratios?
Make sure you are comfortable with Compound Interest, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Ratios?
Reversing the order, or confusing part-to-part (2:3) with part-to-whole (2/5).
How can I practise Ratios?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Ratios?
Move on to Proportions next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.