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Questions and Answers
Tonya works 60 hours every 3 weeks. If this rate remains constant, which proportion can be used to correctly calculate the number of hours, $x$, she will work in 12 weeks?
Tonya works 60 hours every 3 weeks. If this rate remains constant, which proportion can be used to correctly calculate the number of hours, $x$, she will work in 12 weeks?
- $\frac{60}{x} = \frac{12}{3}$
- $\frac{60}{3} = \frac{12}{x}$
- $\frac{3}{60} = \frac{12}{x}$
- $\frac{60}{3} = \frac{x}{12}$ (correct)
A store sells pens at a rate of 3 pens for $2.70. If a customer wants to buy 10 pens, which method correctly calculates the total cost?
A store sells pens at a rate of 3 pens for $2.70. If a customer wants to buy 10 pens, which method correctly calculates the total cost?
- Divide 10 by 3 to find the number of sets, then multiply the result by $2.70.
- Add $2.70 three times and then add $1.90.
- Multiply 10 by $2.70, then divide the result by 3.
- Find the cost of one pen by dividing $2.70 by 3, then multiply the result by 10. (correct)
Understanding unit rates is essential for making informed decisions. In which of the following scenarios is calculating a unit rate MOST helpful?
Understanding unit rates is essential for making informed decisions. In which of the following scenarios is calculating a unit rate MOST helpful?
- Comparing the prices of different-sized packages of the same product. (correct)
- Measuring the volume of water in a fish tank.
- Calculating the area of a circular rug.
- Determining the perimeter of a rectangular garden.
Which of the following statements accurately describes the relationship between ratios, unit rates, and equivalent fractions?
Which of the following statements accurately describes the relationship between ratios, unit rates, and equivalent fractions?
A recipe requires 2 cups of flour for every 3 eggs. If a baker wants to use 9 eggs, how many cups of flour are needed to maintain the same ratio?
A recipe requires 2 cups of flour for every 3 eggs. If a baker wants to use 9 eggs, how many cups of flour are needed to maintain the same ratio?
What distinguishes a rate from a ratio?
What distinguishes a rate from a ratio?
If a store sells 15 blue pens for every 5 red pens, which of the following is the simplified ratio of blue pens to red pens?
If a store sells 15 blue pens for every 5 red pens, which of the following is the simplified ratio of blue pens to red pens?
A car travels 300 miles in 6 hours. What is the unit rate of the car's speed?
A car travels 300 miles in 6 hours. What is the unit rate of the car's speed?
A pack of 6 bottles of water costs $3.60. What is the unit price per bottle?
A pack of 6 bottles of water costs $3.60. What is the unit price per bottle?
Which of the following scenarios involves a rate rather than a ratio?
Which of the following scenarios involves a rate rather than a ratio?
If a recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, what amount of sugar is needed if 5 cups of flour are used?
If a recipe calls for a ratio of 2 cups of flour to 1 cup of sugar, what amount of sugar is needed if 5 cups of flour are used?
A school has 15 teachers for every 200 students. If the school has 1000 students, how many teachers should it have to maintain the same ratio?
A school has 15 teachers for every 200 students. If the school has 1000 students, how many teachers should it have to maintain the same ratio?
A store sells two brands of juice. Brand A costs $4.50 for a 64-ounce bottle, and Brand B costs $3.20 for a 48-ounce bottle. Which brand offers the lower unit price?
A store sells two brands of juice. Brand A costs $4.50 for a 64-ounce bottle, and Brand B costs $3.20 for a 48-ounce bottle. Which brand offers the lower unit price?
Flashcards
What is a ratio?
What is a ratio?
A comparison of two quantities (numbers or measurements).
Terms of a ratio
Terms of a ratio
The numbers being compared in a ratio.
What is a rate?
What is a rate?
A ratio comparing two quantities with different units.
What is a unit rate?
What is a unit rate?
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What is unit price?
What is unit price?
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How to calculate unit Price?
How to calculate unit Price?
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How to find a unit rate?
How to find a unit rate?
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Example of rates?
Example of rates?
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Unit Rate
Unit Rate
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Equivalent Ratios
Equivalent Ratios
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Ratio
Ratio
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Rate
Rate
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Finding Equal Ratios
Finding Equal Ratios
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Study Notes
- Ratios and rates are key to middle school mathematics and algebra readiness.
Ratios
- A ratio compares two numbers or measurements.
- The terms of a ratio are the numbers or measurements being compared.
- For instance, if a store has 6 red shirts and 8 green shirts, the ratio of red to green shirts is 6 to 8.
- This ratio can be written as 6 red/8 green, 6 red:8 green, or simply 6/8 or 6:8.
- All of these expressions mean there are 6 red shirts for every 8 green shirts.
- Ratios can be rewritten as fractions, such as 6/8 becoming 3/4.
Rates
- A rate is a special ratio where the two terms are in different units.
- For example, a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.
- The first term (69¢) is measured in cents, and the second term (12) in ounces.
- This rate can be written as 69¢/12 ounces or 69¢:12 ounces.
- Both expressions mean that 69¢ is paid for every 12 ounces of corn.
- Rates can be used in calculations as fractions, such as 69/12, creating a new unit: cents per ounce.
- Rates are commonly used, such as working 40 hours per week or earning interest annually.
Unit Rates
- Unit rates are rates expressed as a quantity of 1.
- Examples of unit rates are 2 feet per second or 5 miles per hour.
- Any rate can be written as a unit rate by reducing the fraction to have 1 as the denominator.
- For example, 120 students for every 3 buses can be expressed as a unit rate of 40 students per bus.
Unit Price
- Unit price is when a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can.
- To find the unit price from a non-unit price, divide the terms of the ratio.
- For example, if $5.50 is paid for 5 pounds of potatoes, the unit price is $1.10 per pound.
Problem Solving with Rates
- Rates and unit rates help to solve real-world problems.
- For example: Tonya works 60 hours every 3 weeks. At that rate, how many hours will she work in 12 weeks?
- To solve this, write a ratio equal to 60/3 with a second term of 12, which becomes 240/12, showing that Tonya will work 240 hours in 12 weeks.
- When finding equal ratios, remember to multiply or divide both terms of the ratio by the same number.
- Example unit price problem: A sign in a store says 3 Pens for $2.70. How much would 10 pens cost?
- To solve this, find the unit price of the pens, then multiply by 10.
Standards
- Core Standard: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0. (6.RP.A.2)
- Prerequisite Skills: Understanding of ratios, writing ratios, simplifying ratios, working with fractions, and finding equivalent fractions.
- Standard: Use ratio and rate reasoning to find equivalent ratios and solve real-world problems (6.RP.A.3)
- Finding equivalent ratios uses the same thought process as finding equivalent fractions.
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Description
Explore ratios as comparisons between two numbers or measurements, such as red shirts to green shirts. Discover how ratios can be expressed and simplified as fractions. Learn about rates as special ratios with different units, like cost per ounce, and their use in calculations.
