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.
Let's first check whether 2088 feet per minute is the same as 696 meters per minute. To do so, we will calculate how many meters per minute are equal to 2088 feet per minute. Let's convert feet per minute into meters per minute.
2088 ft/1 min=m/1 min
We can do this by using the fact that 1 meter equals 3.281 feet. Let's write this relationship as a unit ratio.
3.281 ft/1m
To perform the conversion, we need to multiply the unit rate 2088ft1min by the unit ratio or its reciprocal. Remember, we want to arrange these ratios such that every unit we do not want gets canceled out and only the units that we want will remain.
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
We got that 2088 feet per minute is equal to about 636 meters per minute. This means that the unit rate from option A is not the same as 2088 feet per minute.
Next, we will check whether 2088 feet per minute is the same as 696 yards per minute. To do so, we will calculate how many yards per minute are equal to 2088 feet per minute. This means that we need to change feet per minute into yards per minute. 2088 ft/1 min=yd/1 min We can do this by using the fact that 1 yard equals 3 feet. Let's write this relationship as a unit ratio. 3 ft/1yd To perform the conversion, we need to multiply the unit rate 2088ft1min by the unit ratio or its reciprocal. Remember, we want to arrange these ratios such that every unit we do not want gets canceled out and only the units that we want will remain.
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
We got that 2088 feet per minute is equal to about 696 yards per minute. This means that the unit rate from option B is the same as 2088 feet per minute.
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 |
To perform the conversion, we need to multiply the unit rate 2088ft1min by each unit ratio or its reciprocal. Remember, we want to arrange these ratios such that every unit we do not want gets canceled out and only the units that we want will remain.
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
We got that 2088 feet per minute is equal to 11.6 yards per second. This means that the unit rate from option D is not the same as 2088 feet per minute.
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.