Mid-Chapter Check
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When multiplying conversion factors, make sure the only remaining units are the desired units.
B
We are asked to determine which of the given unit rates is the same as 2088 feet per minute. We will consider each option one at a time.
Multiply fractions
Cancel out common factors
Simplify quotient
Identity Property of Multiplication
Write as a product of fractions
a/b=.a /3.281./.b /3.281.
Use a calculator
Round to nearest integer
Multiply fractions
Multiply fractions
Cancel out common factors
Simplify quotient
Identity Property of Multiplication
Write as a product of fractions
a/b=.a /3./.b /3.
Use a calculator
Multiply fractions
Note that the unit rate from option C has the same units as 2088 feet per minute. Since 2088≠ 696, these unit rates are not equivalent.
Finally, we will check whether 2088 feet per minute is the same as 696 yards per second. To do so, we will calculate how many yards per second are equal to 2088 feet per minute. This means that we need to change feet per minute into yards per second. 2088 ft/1 min=yards/1 second Let's start by organizing the relationships between the units in a table.
| Starting Unit | Converted Unit | Unit Ratio |
|---|---|---|
| 3 feet | 1 yard | 3ft/1yd |
| 1 minute | 60 seconds | 60sec/1min |
Multiply fractions
Cancel out common factors
Simplify quotient
Multiply
Write as a product of fractions
a/b=.a /180./.b /180.
Use a calculator
Multiply fractions
As we can see, only the unit rate from option B is the same as 2088 feet per minute. This means that the correct option is B.