How far in one hour. Which bag of peaches. Miles, then kilometers.
A rate compares two amounts measured in different units. For example, 180 miles in 3 hours compares distance with time. A price of $18 for 12 tacos compares money with the number of tacos.
A unit rate tells the amount for one unit: miles in one hour, or dollars for one taco. To compare two speeds or prices, use the same units for both.
You get there by dividing. 180 ÷ 3 = 60. Sixty miles in one hour.
Fractions still divide. Dividing by a fraction means multiply by the flip — switch the top and the bottom. 3/4 ÷ 1/2 is 3/4 × 2/1, which is 3/2. One and a half.
Try it. Then open the steps.
Example 1 of 6
Family car, Texas highway
A car covers 215 miles in 5 hours at a constant speed. What is the unit rate in miles per hour?
| Hours | Miles |
|---|---|
| 1 | ? |
| 5 | 215 |
Answer: 43 miles per hour
Example 2 of 6
Friday night, the window
Five tacos cost $12.50. What is the cost of one taco?
Answer: $2.50 per taco
Example 3 of 6
Around the block
You walk 3/4 of a mile in 1/2 of an hour. What is the unit rate in miles per hour?
Answer: 1.5 miles per hour
Example 4 of 6
Saturday, the shop on the corner
Three scoops cost $8.25. What does one scoop cost?
Answer: $2.75 per scoop
Example 5 of 6
After the match, walking to the car
A soccer player took 18 shots across 5 games. What was the average number of shots per game?
Answer: 3.6 shots per game
Example 6 of 6
Produce aisle
Nine pounds of peaches cost $45. What is the price of one pound?
Answer: $5 per pound
Easy to miss: Dividing hours by miles when the question asks for miles per hour.
Do this: Ask which unit should come after “per.” For miles per hour, divide miles by hours. Hours per mile tells the time for one mile—a different rate.
Easy to miss: Stopping at the fraction and never simplifying.
Do this: A unit rate can be a mixed number or a decimal. 2.5 miles per minute is fine. So is 5/2.
28 problems · Camp, Trail, Summit
