Podcast
Questions and Answers
A store is selling pencils. A pack of 12 pencils costs $3.60 while individual pencils cost $0.35 each. How much money do you save by buying a pack instead of 12 individual pencils?
A store is selling pencils. A pack of 12 pencils costs $3.60 while individual pencils cost $0.35 each. How much money do you save by buying a pack instead of 12 individual pencils?
$0.60
Sarah can knit 8 scarves in 4 weeks. If she continues at the same rate, how many scarves can she knit in 10 weeks?
Sarah can knit 8 scarves in 4 weeks. If she continues at the same rate, how many scarves can she knit in 10 weeks?
20 scarves
A factory produces 350 toys in 5 hours. How many toys can it produce in 1 hour? How many can it produce in 9 hours?
A factory produces 350 toys in 5 hours. How many toys can it produce in 1 hour? How many can it produce in 9 hours?
70 toys in 1 hour, 630 toys in 9 hours
A car travels 240 miles on 8 gallons of gas. How many miles per gallon does the car get? How far can it travel on 12 gallons of gas?
A car travels 240 miles on 8 gallons of gas. How many miles per gallon does the car get? How far can it travel on 12 gallons of gas?
A baker uses 3 cups of sugar for every 2 cakes he bakes. How much sugar does he need to bake 7 cakes?
A baker uses 3 cups of sugar for every 2 cakes he bakes. How much sugar does he need to bake 7 cakes?
A farmer harvests 56 apples from 8 trees. At this rate, how many apples can they expect to harvest if they have 20 trees?
A farmer harvests 56 apples from 8 trees. At this rate, how many apples can they expect to harvest if they have 20 trees?
Liam reads 120 pages of a book in 4 days. Emma reads 105 pages in 3 days. Who reads more pages per day?
Liam reads 120 pages of a book in 4 days. Emma reads 105 pages in 3 days. Who reads more pages per day?
A water tank is filled with 63 gallons of water in 7 minutes. At what rate is the tank being filled per minute? How long will it take to fill the tank with 99 gallons?
A water tank is filled with 63 gallons of water in 7 minutes. At what rate is the tank being filled per minute? How long will it take to fill the tank with 99 gallons?
A store sells a pack of 6 pens for $7.50, while another store sells a pack of 8 of the same pens for $9.60. Which pack offers a better deal in terms of cost per pen?
A store sells a pack of 6 pens for $7.50, while another store sells a pack of 8 of the same pens for $9.60. Which pack offers a better deal in terms of cost per pen?
A cyclist travels 45 miles in 3 hours. What is the cyclist's average speed in miles per hour? How long will it take the cyclist to travel 75 miles at the same rate?
A cyclist travels 45 miles in 3 hours. What is the cyclist's average speed in miles per hour? How long will it take the cyclist to travel 75 miles at the same rate?
John earns $80 for working 8 hours, while Jane earns $108 for working 9 hours. Who earns more per hour, and by how much?
John earns $80 for working 8 hours, while Jane earns $108 for working 9 hours. Who earns more per hour, and by how much?
A bakery sells a box of 12 cookies for $18 and a smaller box of 5 cookies for $8. Which box offers a better value in terms of price per cookie?
A bakery sells a box of 12 cookies for $18 and a smaller box of 5 cookies for $8. Which box offers a better value in terms of price per cookie?
A store sells a 5-pound bag of flour for $6.00. They also sell a 2-pound bag of the same flour for $2.50. Which is the better deal?
A store sells a 5-pound bag of flour for $6.00. They also sell a 2-pound bag of the same flour for $2.50. Which is the better deal?
A car can travel 320 miles on 10 gallons of fuel. How far can it travel on 1 gallon of fuel? How far can it travel on 15 gallons of fuel?
A car can travel 320 miles on 10 gallons of fuel. How far can it travel on 1 gallon of fuel? How far can it travel on 15 gallons of fuel?
A worker is paid $102 for 6 hours of work. At the same hourly rate, how much would they be paid for 9 hours of work?
A worker is paid $102 for 6 hours of work. At the same hourly rate, how much would they be paid for 9 hours of work?
If 7 tickets to a concert cost $84, what is the price per ticket? How much would 12 tickets cost?
If 7 tickets to a concert cost $84, what is the price per ticket? How much would 12 tickets cost?
Flashcards
Unit Rate
Unit Rate
The rate for a single unit of something.
Unit Rate Formula
Unit Rate Formula
Rate = Quantity / Unit
Price per item
Price per item
Finding the cost of a single item.
Distance per time
Distance per time
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Earnings per hour
Earnings per hour
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Items per group
Items per group
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Cost per unit of measure
Cost per unit of measure
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Apples cost $2.50, cost per apple?
Apples cost $2.50, cost per apple?
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What is unit cost?
What is unit cost?
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What is speed?
What is speed?
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What is hourly wage?
What is hourly wage?
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What is 'better deal'?
What is 'better deal'?
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What is production rate?
What is production rate?
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What is comparing speed?
What is comparing speed?
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What are savings?
What are savings?
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What is proportional scaling?
What is proportional scaling?
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Study Notes
- Unit rate problems involve finding the rate for a single unit of something.
- Unit rates are useful for comparing different deals or understanding relationships between quantities.
- The basic formula for a unit rate is: Rate = Quantity / Unit.
Types of Unit Rate Problems
- Price per item: Finding the cost of one item when given the price for multiple items.
- Distance per time: Calculating speed (miles per hour, kilometers per minute).
- Earnings per hour: Determining how much money is earned for one hour of work.
- Items per group: Finding how many items are in one group or set.
- Cost per unit of measure: Calculating cost per ounce, pound, liter, etc.
Examples Problems
- Problem: If 5 apples cost $2.50, what is the cost of one apple?
- Solution: $2.50 / 5 apples = $0.50 per apple.
- Problem: A car travels 120 miles in 2 hours. What is its speed in miles per hour?
- Solution: 120 miles / 2 hours = 60 miles per hour.
- Problem: Sarah earns $48 for working 6 hours. How much does she earn per hour?
- Solution: $48 / 6 hours = $8 per hour.
- Problem: There are 36 cookies in 3 boxes. How many cookies are in one box?
- Solution: 36 cookies / 3 boxes = 12 cookies per box.
- Problem: A 2-liter bottle of soda costs $2.80. What is the cost per liter?
- Solution: $2.80 / 2 liters = $1.40 per liter.
Practice Problems
- Problem: If 8 notebooks cost $16, what is the cost of one notebook?
- Solution: $16 / 8 notebooks = $2 per notebook
- Problem: A train travels 300 miles in 5 hours. What is its speed in miles per hour?
- Solution: 300 miles / 5 hours = 60 miles per hour.
- Problem: John earns $63 for working 7 hours. How much does he earn per hour?
- Solution: $63 / 7 hours = $9 per hour.
- Problem: There are 45 pencils in 5 packs. How many pencils are in one pack?
- Solution: 45 pencils / 5 packs = 9 pencils per pack.
- Problem: A 3-pound bag of oranges costs $4.50. What is the cost per pound?
- Solution: $4.50 / 3 pounds = $1.50 per pound.
- Problem: If 4 movie tickets cost $36, what is the cost of one ticket?
- Solution: $36 / 4 tickets = $9 per ticket.
- Problem: A plane flies 1500 miles in 3 hours. What is its speed in miles per hour?
- Solution: 1500 miles / 3 hours = 500 miles per hour.
- Problem: Emily earns $56 for working 8 hours. How much does she earn per hour?
- Solution: $56 / 8 hours = $7 per hour.
- Problem: There are 24 crayons in 2 boxes. How many crayons are in one box?
- Solution: 24 crayons / 2 boxes = 12 crayons per box.
- Problem: A 5-gallon container of water costs $12.50. What is the cost per gallon?
- Solution: $12.50 / 5 gallons = $2.50 per gallon.
- Problem: If 6 erasers cost $4.20, what is the cost of one eraser?
- Solution: $4.20 / 6 erasers = $0.70 per eraser.
- Problem: A cyclist travels 54 miles in 3 hours. What is the cyclist's speed in miles per hour?
- Solution: 54 miles / 3 hours = 18 miles per hour.
- Problem: David earns $81 for working 9 hours. How much does he earn per hour?
- Solution: $81 / 9 hours = $9 per hour.
- Problem: There are 56 stickers in 7 sheets. How many stickers are in one sheet?
- Solution: 56 stickers / 7 sheets = 8 stickers per sheet.
- Problem: A 4-quart container of milk costs $6.00. What is the cost per quart?
- Solution: $6.00 / 4 quarts = $1.50 per quart.
More Challenging Problems
- Problem: Supermarket A sells 3 cans of beans for $2.70, and Supermarket B sells 5 cans of the same beans for $4.00. Which supermarket has the better deal?
- Solution:
- Supermarket A: $2.70 / 3 cans = $0.90 per can
- Supermarket B: $4.00 / 5 cans = $0.80 per can
- Supermarket B has the better deal.
- Solution:
- Problem: A printer prints 480 pages in 8 minutes. How many pages can it print in 1 minute? How many pages can it print in 15 minutes?
- Solution:
- Pages per minute: 480 pages / 8 minutes = 60 pages per minute
- Pages in 15 minutes: 60 pages/minute * 15 minutes = 900 pages
- Solution:
- Problem: Two friends are running a race. John runs 2 miles in 20 minutes, and Mary runs 3 miles in 33 minutes. Who is running faster?
- Solution:
- John: 20 minutes / 2 miles = 10 minutes per mile
- Mary: 33 minutes / 3 miles = 11 minutes per mile
- John is running faster (lower time per mile).
- Solution:
- Problem: A store sells a pack of 6 bottles of juice for $4.20. Individually, each bottle costs $0.80. How much do you save by buying a pack instead of 6 individual bottles?
- Solution:
- Cost of 6 individual bottles: 6 bottles * $0.80/bottle = $4.80
- Savings: $4.80 - $4.20 = $0.60
- Solution:
- Problem: A recipe requires 2 cups of flour for every 16 cookies. How much flour is needed to make 40 cookies?
- Solution:
- Cookies per cup: 16 cookies / 2 cups = 8 cookies per cup
- Cups needed: 40 cookies / 8 cookies per cup = 5 cups
- Solution:
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Description
Explore the concept of unit rates and their applications in real-world scenarios like calculating price per item and speed. Learn how to solve various types of unit rate problems. Understand the formula: Rate = Quantity / Unit.
