Exploring Rates and Unit Rates

The video tutorial by Jeff Jacobson explains the concept of rates, highlighting their distinction from ratios by emphasizing the presence of units. It introduces the idea of unit rates, where one of the quantities is one, and provides examples to illustrate the calculation of unit rates. The examples include determining the speed of an asteroid, the cost of salmon, and the cost of halit using different methods such as ratio tables and double line graphs.

What distinguishes a rate from a ratio?

• Rates and ratios are exactly the same.

• Rates involve quantities with different units.

• Rates have no units, while ratios do.

• Ratios involve quantities with the same units.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

What is a unit rate?

• A rate that cannot be simplified further.

• A rate where one of the quantities is one.

• A rate with units in the numerator only.

• A rate with units in the denominator only.

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CCSS.6.RP.A.1

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What is the purpose of simplifying a rate to a unit rate?

• To find the cost for one unit of quantity.

• To compare two rates directly.

• To increase the complexity of the rate.

• To remove all units from the rate.

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CCSS.6.RP.A.1

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What does a unit rate allow you to compare?

• Two quantities without units.

• The cost of multiple units.

• A quantity to one unit of another quantity.

• The total units in a ratio.

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CCSS.6.RP.A.1

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How do you calculate the unit rate of an asteroid traveling 5 miles every 8 seconds to find its speed per second?

• Multiply 5 miles by 8 seconds.

• Divide 5 miles by 8 seconds.

• Add 5 miles to 8 seconds.

• Subtract 8 seconds from 5 miles.

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CCSS.6.RP.A.1

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How can a ratio table help in finding a unit rate?

• By subtracting one quantity from another.

• By multiplying the quantities by each other.

• By dividing the given quantity to reach one unit.

• By adding quantities until reaching one unit.

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CCSS.6.RP.A.1

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If a chef buys 6 pounds of salmon for $51, how much does one pound cost?

• $8.50

• $6.00

• $9.00

• $7.50

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CCSS.6.RP.A.3B

If 6 pounds of salmon cost $51, how much would 9 pounds cost?

• $102.00

• $76.50

• $85.00

• $68.00

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CCSS.6.RP.A.3B

Using a double line graph, how can you determine the cost for 7 pounds of halibut if 2 pounds cost $16?

• By dividing $16 by 7

• By multiplying $16 by 7

• By finding the rate for one pound and then multiplying by 7

• By adding $16 for every two pounds until reaching 7 pounds

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CCSS.6.RP.A.3B

What is the advantage of using a double line graph for calculating rates?

• It visually represents the relationship between two quantities.

• It eliminates the need for units in rates.

• It simplifies the calculation of complex rates.

• It increases the calculation speed for all rates.

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CCSS.6.RP.A.3B