Algebra
Expressions
Units and quantities
20 practice questions
1 video lesson
Theory + worked examples
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20 questions
Practice questions
Every question with a fully worked solution.
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1 video(s)
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Theory
A quantity is a number with a unit. Units guide the arithmetic:
- Add or subtract only quantities with the same unit.
- Multiply or divide units too: \(\dfrac{\text{mi}}{\text{hr}}\) is a speed.
- Choose a scale appropriate to the size of the data.
Track units through a calculation — they confirm the answer makes sense.
Working with units and quantities.
Unit analysis in action.
Units combine like numbers:
\[\dfrac{\text{miles}}{\text{hour}}\times\text{hours}=\text{miles}\]
The units of the answer follow from the operation.
How to work with units
- Attach a unit to every quantity.
- Match units before adding or subtracting.
- Multiply/divide the units along with the numbers.
- Pick a scale that fits the quantity.
Example 1 — A rate
A car goes \(120\) miles in \(2\) hours. Find its speed with units.
Solution
Divide distance by time.
| \(\dfrac{120\text{ mi}}{2\text{ hr}}\) | \(=\) | \(60\text{ mph}\) |
Example 2 — Multiply by a rate
At \(15\) dollars per hour, how much for \(6\) hours?
Solution
Multiply the rate by the hours.
| \(15\dfrac{\$}{\text{hr}}\times 6\text{ hr}\) | \(=\) | \(\$90\) |
Example 3 — Matching units
Can you add \(3\) meters and \(50\) centimeters directly?
Solution
Convert first: \(50\) cm \(=0.5\) m.
| \(3\text{ m}+0.5\text{ m}\) | \(=\) | \(3.5\text{ m}\) |
Example 4 — Choose a scale
What units suit measuring a city's population?
Solution
Use thousands or millions of people — a scale that fits the size of the quantity.
Common pitfalls
Match units before adding — convert first if needed.
Carry units through multiplication and division.
Pick a sensible scale for the size of the data.
Frequently asked questions
Why attach units to quantities?
Units give the number meaning and confirm the calculation makes sense.
When can you add two quantities?
Only when they have the same unit.
How do units behave when you divide?
They divide too — miles ÷ hours gives miles per hour.
What is a rate?
A quantity per unit of another, like miles per hour.
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