1.10 Systems of measurement  (Page 2/13)

When we use the identity property of multiplication to convert units, we need to make sure the units we want to change from will divide out. Usually this means we want the conversion fraction to have those units in the denominator.

Ndula, an elephant at the San Diego Safari Park, weighs almost 3.2 tons. Convert her weight to pounds.

Solution

We will convert 3.2 tons into pounds. We will use the identity property of multiplication, writing 1 as the fraction $\frac{2000\text{pounds}}{1\text{ton}}.$

	$\text{3.2 tons}$
Multiply the measurement to be converted, by 1.	$\text{3.2 tons}\cdot 1$
Write 1 as a fraction relating tons and pounds.	$\text{3.2 tons}\cdot \frac{\text{2,000 pounds}}{\text{1 ton}}$
Simplify.
Multiply.	$\text{6,400 pounds}$
	Ndula weighs almost 6,400 pounds.

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Sometimes, to convert from one unit to another, we may need to use several other units in between, so we will need to multiply several fractions.

Juliet is going with her family to their summer home. She will be away from her boyfriend for 9 weeks. Convert the time to minutes.

Solution

To convert weeks into minutes we will convert weeks into days, days into hours, and then hours into minutes. To do this we will multiply by conversion factors of 1.

	9 weeks
Write $1$ as $\frac{\text{7 days}}{\text{1 week}}$ , $\frac{\text{24 hours}}{\text{1 day}}$ , and $\frac{\text{60 minutes}}{\text{1 hour}}$ .	$\frac{\text{9 wk}}{1}\cdot \frac{\text{7 days}}{\text{1 wk}}\cdot \frac{\text{24 hr}}{\text{1 day}}\cdot \frac{\text{60 min}}{\text{1 hr}}$
Divide out the common units.
Multiply.	$\frac{9\cdot 7\cdot 24\cdot \text{60 min}}{1\cdot 1\cdot 1\cdot 1}$
Multiply.	$\text{90,720 min}$

Juliet and her boyfriend will be apart for 90,720 minutes (although it may seem like an eternity!).

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How many ounces are in 1 gallon?

Solution

We will convert gallons to ounces by multiplying by several conversion factors. Refer to [link] .

	1 gallon
Multiply the measurement to be converted by 1.	$\frac{\text{1 gallon}}{1}\cdot \frac{\text{4 quarts}}{\text{1 gallon}}\cdot \frac{\text{2 pints}}{\text{1 quart}}\cdot \frac{\text{2 cups}}{\text{1 pint}}\cdot \frac{\text{8 ounces}}{\text{1 cup}}$
Use conversion factors to get to the right unit. Simplify.
Multiply.	$\frac{1\cdot 4\cdot 2\cdot 2\cdot \text{8 ounces}}{1\cdot 1\cdot 1\cdot 1\cdot 1}$
Simplify.	$\text{128 ounces}$ There are 128 ounces in a gallon.

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Use mixed units of measurement in the u.s. system

We often use mixed units of measurement in everyday situations. Suppose Joe is 5 feet 10 inches tall, stays at work for 7 hours and 45 minutes, and then eats a 1 pound 2 ounce steak for dinner—all these measurements have mixed units.

Performing arithmetic operations on measurements with mixed units of measures requires care. Be sure to add or subtract like units!

Seymour bought three steaks for a barbecue. Their weights were 14 ounces, 1 pound 2 ounces and 1 pound 6 ounces. How many total pounds of steak did he buy?

Solution

We will add the weights of the steaks to find the total weight of the steaks.

Add the ounces. Then add the pounds.
Convert 22 ounces to pounds and ounces.	$$ 2 pounds + 1 pound, 6 ounces
Add the pounds.	$$ 3 pounds, 6 ounces
	Seymour bought 3 pounds 6 ounces of steak.

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