Rate
In short: Rate is a comparison by division between amounts counted in unlike units, for instance 180 words typed in 4 minutes or 96 miles driven on 3 gallons of gas.
6th GradeRatios and Percents6.RP.A.2
What is Rate?
A rate tells how much of one kind of thing happens for a certain amount of another kind. Typing speed, gas mileage and heart beats per minute are all rates, because each links two different units.
Precisely, it has the form \(\frac{a \text{ units of one kind}}{b \text{ units of another kind}}\). Dividing by \(b\) gives the amount for exactly one unit of the second quantity.
How to spot it
- A phrase puts “per”, “each” or “every” between two unlike units, like dollars per pound.
- A situation describes speed, price, pay or fuel use over time or distance.
- You are told what happens in a long stretch and asked about a shorter or longer stretch.
- Two quantities with different labels, such as pages and minutes, appear in one sentence.
The method
- Identify the two quantities and their units, and decide which one goes on top.
- Write the comparison as a fraction with the units attached, such as \(\frac{180 \text{ words}}{4 \text{ minutes}}\).
- Simplify or divide to get the amount per one unit when a single-unit comparison is needed.
- Multiply the result by a new amount of the second unit to predict a new total.
Rate: solved example
Problem
Priya types 252 words in 6 minutes at a steady speed. How many words can she type in 15 minutes?
Solution
Her speed is \(\frac{252 \text{ words}}{6 \text{ minutes}} = 42\) words per minute.
Multiply by the new time: \(42 \times 15 = 630\). Priya can type 630 words in 15 minutes.
Try it
Question 1
A cargo van drives 408 miles on 17 gallons. Write the fuel rate in miles per gallon.
Show the answer
\(408 \div 17 = 24\), so the van gets 24 miles per gallon.
Question 2
A lifeguard earns $93.75 for 7.5 hours. How much does she earn per hour?
Show the answer
\(93.75 \div 7.5 = 12.5\), so she earns \$12.50 per hour.
Rate vs. Ratio
A ratio can compare any two quantities, even two counts of one kind such as 3 hats to 5 scarves. A rate always pairs unlike units, so its answer carries a phrase like miles per hour.
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Whole dictionary: A–Z · 6th Grade · Ratios and Percents