Ratios and unit rates
The idea
A ratio compares quantities. A unit rate expresses one quantity per one unit of another. Keep units attached to numbers so the result has meaning. Equivalent ratios preserve the same multiplicative relationship.
Worked example
Four notebooks cost $12. Divide both quantities by four: one notebook costs $3. Seven notebooks at the same rate cost $21. This assumes there is no separate fee or bulk discount.
Another application
If three pencils cost $1.80, the unit price is $0.60 per pencil. A five-pencil pack costing $3.25 is $0.65 per pencil, so the smaller pack costs less per pencil even though it contains fewer items.
A common misunderstanding
Dividing in the wrong order changes the units. Cost divided by meters gives cost per meter; meters divided by cost gives meters per dollar.
Try it yourself
Invent two snack offers with different package sizes. Calculate price per item before deciding which costs less per item.
Check your understanding
Six meters of ribbon cost $15. What is the price per meter?
Reveal the explained answer
$2.50 per meter: 15 divided by 6.