Rates and Unit Rates
A ratio comparing different units, reduced to per-one.
Key idea
A ratio comparing different units, reduced to per-one.
In depth
A rate compares quantities with different units (km per hour, price per kg). A unit rate has 1 in the denominator, making comparison easy: find the cost or distance for one unit.
Worked example
120 km in 1.5 hours: 120 ÷ 1.5 = 80 km/h.
Formula
Real-world uses
- Comparing supermarket prices per 100 g
- Calculating fuel economy in miles per gallon
- Wage per hour
Common mistake
Dividing in the wrong direction. Check the units: km ÷ h gives km/h.
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 Rates and Unit Rates?
A ratio comparing different units, reduced to per-one. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Rates and Unit Rates?
The key formula is speed = distance / time.
Where is Rates and Unit Rates used in real life?
Real-world examples: Comparing supermarket prices per 100 g; Calculating fuel economy in miles per gallon; Wage per hour.
What should I learn before Rates and Unit Rates?
Make sure you are comfortable with Proportions, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Rates and Unit Rates?
Dividing in the wrong direction. Check the units: km ÷ h gives km/h.
How can I practise Rates and Unit Rates?
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 Rates and Unit Rates?
Move on to Direct Proportion 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.