Unit Rates

Grade 6 · mathematics · 141 practice problems · read aloud

🔊 Listen to this explanation

What is a Unit Rate? 🤔

A unit rate is a ratio that compares two different quantities where the second term is 1. It tells you the amount of one thing for a single unit of another. We use unit rates all the time in real life to compare prices (like cost per item), speed (miles per hour), and more!

How to Find a Unit Rate: Step-by-Step

  1. Identify the two quantities you are comparing.
  2. Write the ratio as a fraction (e.g., cost / items, miles / hours).
  3. Divide the numerator by the denominator to find the price, speed, or amount for just one unit.
  4. Don't forget to write the units in your final answer!

Visual Examples

Example 1: Price per Can

A 6-pack of soda costs $7.50. What is the cost per can?

  1. Ratio: $7.50 / 6 cans
  2. Divide: 7.50 ÷ 6 = 1.25
  3. Answer: The unit rate is $1.25 per can.

Example 2: Reading Speed

Emily reads 120 pages in 3 hours. How many pages does she read per hour?

  1. Ratio: 120 pages / 3 hours
  2. Divide: 120 ÷ 3 = 40
  3. Answer: The unit rate is 40 pages per hour.

Common Mistakes to Avoid 🚫

Dividing in the wrong order: Always put the quantity you want to find on top (numerator). If you want "miles per hour," miles goes on top.

Forgetting the units: An answer of "5" is meaningless. Is it 5 dollars, 5 miles, or 5 apples? Always write $5 per box or 5 miles per hour.

Misplacing the decimal: Take your time when dividing decimals. Use estimation to check if your answer is reasonable.

Tips & Tricks

Look for "per": The word "per" is a huge clue! It means "for each one" and tells you you're finding a unit rate.

Think "One is the Magic Number": Your goal is always to find out what happens when the second quantity is 1.

Double-Check with Multiplication: If your unit rate is 40 pages/hour, then in 3 hours, you should read 40 x 3 = 120 pages. It works!

How to Practice

  • Become a Shopping Detective: At the grocery store, compare the unit prices on tags to find the best deal.
  • Track Your Speed: If you play a video game for 45 minutes and score 900 points, what is your points-per-minute rate?
  • Use Online Games: Search for "unit rate games" or "ratio blaster" for fun, interactive practice.

Practice problems

6 of the 141, worked through step by step — try them before opening the answer.

1 120 ÷ 24 = ?

Hint: Think about how many times the second number fits into the first number.

Show the answer

Answer: 5

  1. Understand the division. We want to know how many times 24 fits into 120.
  2. One way is to break 120 into smaller parts. Notice that 120 = 12 × 10, and 24 = 12 × 2. So 120 ÷ 24 = (12 × 10) ÷ (12 × 2).
  3. Cancel the common factor of 12. (12 × 10) ÷ (12 × 2) = 10 ÷ 2.
  4. Compute 10 ÷ 2 = 5.
  5. Check: 24 × 5 = 120, which matches the original number. Therefore,

We are solving 120 ÷ 24. the answer is 5.

2 480 ÷ 15 = ?

Hint: Think about how many times the second number fits into the first number evenly

Show the answer

Answer: 32

  1. Set up the division: 480 ÷ 15
  2. 15 × 30 = 450
  3. 480 - 450 = 30
  4. 15 × 2 = 30
  5. 30 + 2 = 32
  6. Check: 15 × 32 = 480

The answer is 32.

3 If a car travels 360 km in 4 hours, what is its speed in km/h?

Hint: To find speed, divide the total distance by the total time taken.

Show the answer

Answer: 90

  1. Identify the given values from the problem. Distance traveled = 360 km Time taken = 4 hours
  2. Substitute the given values into the formula. Speed = 360 km / 4 hours
  3. Perform the division. 360 divided by 4 equals 90.
  4. Write the answer with the correct units. The car's speed is 90 km/h. This means the car travels 90 kilometers for every hour it is driving.

To find the speed in kilometers per hour (km/h), we use the formula: Speed = Distance / Time

4 If a car travels 360 km in 4 hours, what is its unit rate in km/h?

Hint: To find unit rate, divide the total quantity by the total number of units. For example, if you need to find cost per item, divide total cost by number of items.

Show the answer

Answer: 90

  1. Identify the total distance and total time. The car travels 360 km in 4 hours.
  2. The unit rate is found by dividing the total distance by the total time. Unit rate = Total distance / Total time Unit rate = 360 km / 4 hours
  3. Perform the division. 360 divided by 4 equals 90.
  4. State the final answer with units. The car's unit rate is 90 km/h. This means the car travels 90 kilometers every hour.

To find the unit rate in km/h, we need to determine how many kilometers the car travels in one hour.

5 If a car travels 450 km in 5 hours, what is its unit rate in km/h?

Hint: To find the unit rate, divide the total distance by the total time.

Show the answer

Answer: 90

  1. Identify the total distance traveled: 450 km
  2. Identify the total time taken: 5 hours
  3. Calculate the unit rate by dividing distance by time: 450 km ÷ 5 hours
  4. Perform the division: 450 ÷ 5 = 90
  5. The unit rate is 90 km/h.

6 If 3/4 of a pizza costs $12, what is the unit rate per whole pizza?

Hint: Think about what fraction of the pizza the given cost represents, and how to find the cost for the entire pizza.

Show the answer

Answer: 16

  1. Understand the problem. If 3/4 of a pizza costs $12, then we want the cost of 1 whole pizza. This is the unit rate per pizza.
  2. Set up a relationship. Let P = price of one whole pizza. Then (3/4) of P = 12. That is: (3/4) * P = 12.
  3. Solve for P. To isolate P, we can multiply both sides of the equation by the reciprocal of 3/4, which is 4/3. So: P = 12 * (4/3)
  4. Perform the multiplication. First, 12 * 4 = 48. Then, 48 / 3 = 16.
  5. Conclusion. The unit rate per whole pizza is $16. Answer: 16

We are told that 3/4 of a pizza costs $12.

Practise this topic — 10 free problems, no signup →