Ratios & Proportional Relationships
Unit Rates
Finding a unit rate associated with a ratio.
Prerequisites
- Understanding Ratios
Which One Is the Better Deal?
One store sells 3 notebooks for $4.50. Another sells 5 notebooks for $7.00. Before reading on, make a guess — which store has the better price? Notice that it's not obvious at a glance, since neither the notebook counts nor the total prices match up directly.
Definition — Unit Rate
The reason unit rates make comparisons fair is that they strip away however many items happened to be in each group, leaving only the price of a single, identical unit — a quantity that means the exact same thing no matter which store's numbers you started with.
Worked Example — Comparing Prices with Unit Rates
Worked Example — Finding a Unit Rate for Speed
Tip
Common Mistakes
Comparing two total prices directly without first finding a unit rate, such as assuming $7.00 is automatically a worse deal than $4.50 without accounting for how many items each price buys.
Total prices alone don't reveal value when the quantities differ — always divide down to a unit rate before comparing two deals.
Dividing in the wrong direction, such as finding notebooks per dollar when the question asks for dollars per notebook.
Check which quantity the question wants to land on '1 unit of' — that quantity goes in the denominator of the division.
Key Takeaways
- A unit rate compares a quantity to exactly 1 unit of another quantity.
- Finding a unit rate makes comparing two different-sized groups fair, since both are reduced to the same '1 unit' basis.
- A unit rate is found by dividing so the second quantity becomes 1.
Summary
Unit rates strip away group size to make fair comparisons possible. The next lesson organizes several equivalent ratios into a table, making it easy to scale a relationship to any size at once.
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