per — Definition, Formula & Examples
Per means 'for each' or 'for every one.' In math, it tells you to divide one quantity by another, and it appears in rates like miles per hour or price per item.
The word 'per' denotes a ratio of two quantities, indicating division of the first quantity by the second. It expresses how much of one quantity corresponds to exactly one unit of another quantity.
Key Formula
Where:
- = The total amount (e.g., miles, dollars, calories)
- = The unit you are dividing by (e.g., hours, items, servings)
How It Works
Whenever you see the word 'per' between two units, replace it with a division sign. For example, 'miles per hour' means miles divided by hours. This gives you a rate — a single number that describes how two quantities relate to each other. If a car travels 180 miles in 3 hours, you divide 180 by 3 to get 60 miles per hour. The word 'per' always points to the denominator: whatever comes after 'per' is what you divide by.
Worked Example
Problem: A pack of 8 notebooks costs $24. What is the cost per notebook?
Identify the quantities: The total cost is $24 and there are 8 notebooks. 'Per notebook' tells you to divide by the number of notebooks.
Divide: Divide the total cost by the number of notebooks.
State the rate: Attach the units: the result is $3 per notebook.
Answer: The cost is $3 per notebook.
Why It Matters
Understanding 'per' is essential for working with unit rates and unit prices, which appear constantly in proportional reasoning, science classes, and everyday shopping. Careers in healthcare, engineering, and finance rely on rates (dosage per kilogram, cost per square foot, interest per year) that all hinge on this one small word.
Common Mistakes
Mistake: Dividing in the wrong order — for example, dividing hours by miles instead of miles by hours when finding miles per hour.
Correction: The quantity after 'per' is always the denominator. 'Miles per hour' means miles ÷ hours, not the reverse.