Podcast
Questions and Answers
What is the primary purpose of finding a unit rate?
What is the primary purpose of finding a unit rate?
- To compare two quantities with the same units.
- To determine the amount of one quantity per single unit of another quantity. (correct)
- To express a ratio as a percentage.
- To determine the total cost of multiple items.
If a car travels 240 miles in 4 hours, what is the unit rate in miles per hour?
If a car travels 240 miles in 4 hours, what is the unit rate in miles per hour?
- 40 miles per hour
- 50 miles per hour
- 70 miles per hour
- 60 miles per hour (correct)
Apples are priced at $6 for 2 pounds. What is the unit rate in dollars per pound?
Apples are priced at $6 for 2 pounds. What is the unit rate in dollars per pound?
- $12 per pound
- $2 per pound
- $4 per pound
- $3 per pound (correct)
Which method is NOT a valid approach for comparing two ratios?
Which method is NOT a valid approach for comparing two ratios?
Which ratio is greater: 2:3 or 5:8?
Which ratio is greater: 2:3 or 5:8?
Which is a better deal: 5 bananas for $2 or 7 bananas for $3?
Which is a better deal: 5 bananas for $2 or 7 bananas for $3?
What does a unit rate represent?
What does a unit rate represent?
To find the unit rate of 250 miles driven in 5 hours, which calculation should you perform?
To find the unit rate of 250 miles driven in 5 hours, which calculation should you perform?
If 3 notebooks cost $4.50, what is the cost of one notebook?
If 3 notebooks cost $4.50, what is the cost of one notebook?
When comparing ratios using fractions, what must be identical for a valid comparison?
When comparing ratios using fractions, what must be identical for a valid comparison?
Which of the following is an example of calculating a unit rate?
Which of the following is an example of calculating a unit rate?
To compare the ratios 7:10 and 11:15, which common denominator could you use?
To compare the ratios 7:10 and 11:15, which common denominator could you use?
If store A sells 3 pens for $2.70 and store B sells 5 pens for $4.25, which store offers the better deal?
If store A sells 3 pens for $2.70 and store B sells 5 pens for $4.25, which store offers the better deal?
What is the first step in comparing the ratios 4:5 and 7:8?
What is the first step in comparing the ratios 4:5 and 7:8?
A recipe requires a ratio of 2 cups of flour to 3 cups of sugar. If you want to make a larger batch using 8 cups of flour, how many cups of sugar do you need?
A recipe requires a ratio of 2 cups of flour to 3 cups of sugar. If you want to make a larger batch using 8 cups of flour, how many cups of sugar do you need?
What does it mean to say a rate has a denominator of 1?
What does it mean to say a rate has a denominator of 1?
To determine which is traveling faster, car A driving 150 miles in 3 hours or car B driving 220 miles in 4 hours, what should you compare?
To determine which is traveling faster, car A driving 150 miles in 3 hours or car B driving 220 miles in 4 hours, what should you compare?
If a store sells a pack of 6 bottles of water for $3.60, and another store sells a pack of 8 bottles for $4.40, which pack offers water at a lower price per bottle?
If a store sells a pack of 6 bottles of water for $3.60, and another store sells a pack of 8 bottles for $4.40, which pack offers water at a lower price per bottle?
What is the key characteristic of a ratio that distinguishes it from a rate?
What is the key characteristic of a ratio that distinguishes it from a rate?
Which conversion is necessary to compare 2/5 and 35% effectively?
Which conversion is necessary to compare 2/5 and 35% effectively?
Flashcards
What is a ratio?
What is a ratio?
A comparison of two quantities. Can be written as a fraction, with a colon, or using words.
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?
A rate with a denominator of 1, showing the amount of something per single unit of another thing.
How to find a unit rate?
How to find a unit rate?
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What is the unit rate of 120 miles in 3 hours?
What is the unit rate of 120 miles in 3 hours?
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What is the unit rate of $15 for 5 pounds?
What is the unit rate of $15 for 5 pounds?
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How to compare Ratios?
How to compare Ratios?
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Comparing ratios using fractions?
Comparing ratios using fractions?
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Comparing ratios using decimals?
Comparing ratios using decimals?
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Comparing ratios using percentages?
Comparing ratios using percentages?
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Comparing ratios using unit rates?
Comparing ratios using unit rates?
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Which is greater, 3:5 or 4:7?
Which is greater, 3:5 or 4:7?
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Which is a better deal: 6 oranges for $2.50 or 8 oranges for $3.20?
Which is a better deal: 6 oranges for $2.50 or 8 oranges for $3.20?
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Study Notes
- A ratio compares two quantities; it can be written as a fraction, with a colon, or in words.
- A rate is a ratio comparing two quantities of different units.
- A unit rate is a rate with a denominator of 1, expressing the quantity of one item per single unit of another.
Finding Unit Rates
- To find a unit rate, divide the numerator and denominator of the rate by the denominator's value.
- This process simplifies the rate to have 1 as the denominator.
- If travel is 120 miles in 3 hours, the rate is 120 miles / 3 hours.
- To determine the unit rate, divide both the numerator and the denominator by 3: (120 miles / 3) / (3 hours / 3) = 40 miles / 1 hour.
- The resulting unit rate of 40 miles per hour equates to 40 miles traveled for every 1 hour.
- If apples cost 15 dollars for 5 pounds:
- Determine the unit rate by dividing the numerator and the denominator by 5: (15 dollars / 5) / (5 pounds / 5) = 3 dollars / 1 pound.
- The calculation derives a unit rate of 3 dollars per pound, meaning each pound of apples is 3 dollars.
- Unit rates determine the cost per item, speed, or any ratio where one wants to know the amount per single unit.
Comparing Ratios
- Comparable formats to compare ratios are fractions, decimals, or percentages.
- When using fractions, identify a common denominator and compare the numerators.
- The ratio containing the larger numerator will be the greater ratio.
- When using decimals, convert ratios to decimal form by dividing the numerator by the denominator, then compare the values.
- When using percentages, convert ratios to percentages by multiplying the decimal form by 100, then proceed with the comparison.
- An alternative is to find unit rates for each ratio.
- The larger the unit rate, the larger the ratio.
- Ratios 3:5 and 4:7 can be compared like this:
- Both ratios can be converted into fractions: 3/5 and 4/7.
- Find a common denominator, which could be 35: 3/5 = 21/35 and 4/7 = 20/35.
- After comparing the numerators, it is clear that 21/35 is greater than 20/35, meaning 3:5 is greater than 4:7.
- In a comparison of value: 6 oranges for $2.50 versus 8 oranges for $3.20:
- Determine the unit rate for each: $2.50 / 6 oranges ≈ $0.42 per orange, and $3.20 / 8 oranges = $0.40 per orange.
- $0.40 < $0.42, so buying 8 oranges for $3.20 is a better deal.
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