Mathematical Practices

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Monitoring Progress
Exercise name Free?
Monitoring Progress 1 If the population was 280 million in 2000 and 310 million in 2010, then the country grew by 30 million people in 10 years time. 310−2802010−2000​=30 million people=10 years​ We want to know the annual rate of change. This means that we need to know the average number of people added per year. We can use division to find this. 30÷10=3 million people per year​ On average, 3 million people were added per year to the population of the United States.
Monitoring Progress 2 Another way to write "miles per gallon" is as a ratio. gallonmiles​​ This is actually the case any time you see two units separated by the word per. The word per indicates the division of two units. We are told that you drove 240 miles and used 8 gallons of gas. Let's write this as a ratio to calculate your average miles per gallon. 8 gallons240 miles​=30 miles per gallon​
Monitoring Progress 3 Before we can begin thinking about the time it takes for the water to drain from the bathtub, we need to figure out how much water is in the tub. We can calculate this using the formula for volume of a rectangular prism. V=ℓ⋅w⋅h In this formula, ℓ, w, and h represent the length, width, and height of the prism. We are given that the bathtub is 5 ft by 3 ft by 18 inches. We want these to all be the same unit of measurement so we need to convert inches into feet before we calculate the volume. 1 foot12 inches ​⇒1.5 feet18 inches​ Now we can calculate the volume of the bathtub. V=ℓ⋅w⋅hSubstitute valuesV=5⋅3⋅1.5MultiplyV=22.5 The total volume of the bathtub is 22.5 cubic feet. Next, we need to find the amount of water in the bathtub. We are told that it is 43​ full. By multiplying the volume by 43​, we can find the volume of water. 43​VV=22.543​⋅22.5Write as a decimal0.75⋅22.5Use a calculator16.875 Now we know that the bathtub contains 16.875 cubic feet of water. Since the tub drains at 1 cubic feet per minute, it will take about 16.875 minutes to be completely empty.