Percentages
Unit Rates
A unit rate expresses a rate as an amount per single unit – dollars per one item, kilometres per one litre, words per one minute. Reducing any rate down to “per one” makes it instantly comparable to any other rate, no matter how the original quantities were packaged – which is exactly why unit rates are the tool behind smart shopping comparisons, covered in detail in the Best Buy Problems page later in this section.
Finding a Unit Rate
Divide the total amount by the number of units to find the rate for just one unit.
8 kg of apples cost $16. What is the unit rate (cost per kg)?
Unit rate = $16 ÷ 8 kg = $2 per kg.
Comparing Using Unit Rates
Which is the better rate: $18 for 6 items, or $28 for 8 items?
$18 ÷ 6 = $3 per item. $28 ÷ 8 = $3.50 per item. $18 for 6 items is the better (lower) rate.
Real-Life Application
- Grocery shopping: comparing prices across different pack sizes.
- Typing speed: words typed per minute.
- Fuel economy: kilometres travelled per litre of fuel.
Key Takeaways
- A unit rate expresses a comparison “per one” of the second quantity.
- Dividing total by quantity gives the unit rate.
- Unit rates let you fairly compare deals with different package sizes.
Practice: Unit Rates
Find the Unit Rate