9.1 Measurement and the united states system  (Page 2/2)

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For example,

 Equal Measurements Unit Fraction $\text{1ft}=\text{12in.}$ $\frac{\text{1ft}}{\text{12in.}}\text{or}\frac{\text{12in.}}{\text{1ft}}$ $\text{1pt}=\text{16 fl oz}$ $\frac{\text{1pt}}{\text{16 fl oz}}\text{or}\frac{\text{16 fl oz}}{\text{1pt}}$ $\text{1wk}=\text{7da}$ $\frac{\text{7da}}{\text{1wk}}\text{or}\frac{\text{1wk}}{\text{7da}}$

Sample set a

Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.

Convert 11 yards to feet.

Looking in the unit conversion table under length , we see that $1\text{yd}=\text{3 ft}$ . There are two corresponding unit fractions, $\frac{\text{1 yd}}{\text{3 ft}}$ and $\frac{\text{3 ft}}{\text{1 yd}}$ . Which one should we use? Look to see which unit we wish to convert to. Choose the unit fraction with this unit in the numerator . We will choose $\frac{\text{3 ft}}{\text{1 yd}}$ since this unit fraction has feet in the numerator. Now, multiply 11 yd by the unit fraction. Notice that since the unit fraction has the value of 1, multiplying by it does not change the value of 11 yd.

$\begin{array}{cccc}\hfill 11\text{yd}& =& \frac{\text{11}\text{yd}}{1}\cdot \frac{3\text{ft}}{\text{1yd}}\hfill & \text{Divide out common units.}\hfill \\ & =& \frac{11\overline{)\text{yd}}}{1}\cdot \frac{3\text{ft}}{1\overline{)\text{yd}}}\hfill & \text{(Units can be added, subtracted, multiplied, and divided, just as numbers can.)}\hfill \\ & =& \frac{11\cdot 3\text{ft}}{1}\hfill & \\ & =& 33\text{ft}\hfill & \end{array}$

Thus, $11\text{yd}=33\text{ft}$ .

Convert 36 fl oz to pints.

Looking in the unit conversion table under liquid volume , we see that $\text{1 pt}=\text{16 fl oz}$ . Since we are to convert to pints, we will construct a unit fraction with pints in the numerator.

$\begin{array}{cccc}\hfill 36\text{fl oz}& =\hfill & \frac{36\text{fl oz}}{1}\cdot \frac{1\text{pt}}{16\text{fl oz}}& \text{Divide out common units.}\hfill \\ & =& \frac{36\overline{)\text{fl oz}}}{1}\cdot \frac{1\text{pt}}{16\overline{)\text{fl oz}}}\hfill & \\ & =& \frac{36\cdot \text{1 pt}}{16}\hfill & \\ & =& \frac{\text{36 pt}}{16}\hfill & \text{Reduce.}\hfill \\ & =& \frac{9}{4}\text{pt}\hfill & \text{Convert to decimals:}\frac{9}{4}=2.25.\hfill \end{array}$

Thus, $\text{36 fl oz}=\text{2}\text{.}\text{25 pt}$ .

Convert 2,016 hr to weeks.

Looking in the unit conversion table under time , we see that $\text{1wk}=\text{7da}$ and that $1\text{da}=\text{24 hr}$ . To convert from hours to weeks, we must first convert from hours to days and then from days to weeks. We need two unit fractions.

The unit fraction needed for converting from hours to days is $\frac{\text{1 da}}{\text{24 hr}}$ . The unit fraction needed for converting from days to weeks is $\frac{\text{1 wk}}{\text{7 da}}$ .

$\begin{array}{cccc}\hfill 2,016\text{hr}& =& \frac{2,016\text{hr}}{1}\cdot \frac{1\text{da}}{24\text{hr}}\cdot \frac{1\text{wk}}{7\text{da}}\hfill & \text{Divide out common units.}\hfill \\ & =& \frac{2,016\overline{)\text{hr}}}{1}\cdot \frac{1\overline{)\text{da}}}{24\overline{)\text{hr}}}\cdot \frac{1\text{wk}}{7\overline{)\text{da}}}\hfill & \hfill \\ & =& \frac{2,016\cdot 1\text{wk}}{24\cdot 7}\hfill & \text{Reduce.}\hfill \\ & =& 12\text{wk}\hfill & \end{array}$

Thus, $\text{2,016 hr}=\text{12 wk}$ .

Practice set a

Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.

Convert 18 ft to yards.

6 yd

Convert 2 mi to feet.

10,560 ft

Convert 26 ft to yards.

8.67 yd

Convert 9 qt to pints.

18 pt

Convert 52 min to hours.

0.87 hr

Convert 412 hr to weeks.

2.45 wk

Exercises

Make each conversion using unit fractions. If fractions occur, convert them to decimals rounded to two decimal places.

14 yd to feet

42 feet

3 mi to yards

8 mi to inches

506,880 inches

2 mi to inches

18 in. to feet

1.5 feet

84 in. to yards

5 in. to yards

0.14 yard

106 ft to miles

62 in. to miles

0.00 miles (to two decimal places)

0.4 in. to yards

3 qt to pints

6 pints

5 lb to ounces

6 T to ounces

192,000 ounces

4 oz to pounds

15,000 oz to pounds

937.5 pounds

15,000 oz to tons

9 tbsp to teaspoons

27 teaspoons

3 c to tablespoons

5 pt to fluid ounces

80 fluid ounces

16 tsp to cups

5 fl oz to quarts

0.16 quart

3 qt to gallons

5 pt to teaspoons

480 teaspoons

3 qt to tablespoons

18 min to seconds

1,080 seconds

4 days to hours

3 hr to days

$\frac{1}{8}=0\text{.}\text{125}$ day

$\frac{1}{2}$ hr to days

$\frac{1}{2}$ da to weeks

$\frac{1}{\text{14}}=0\text{.}\text{0714}$ week

$3\frac{1}{7}$ wk to seconds

Exercises for review

( [link] ) Specify the digits by which 23,840 is divisible.

1,2,4,5,8

( [link] ) Find $2\frac{4}{5}$ of $5\frac{5}{6}$ of $7\frac{5}{7}$ .

( [link] ) Convert $0\text{.}3\frac{2}{3}$ to a fraction.

$\frac{\text{11}}{\text{30}}$

( [link] ) Use the clustering method to estimate the sum: $\text{53}+\text{82}+\text{79}+\text{49}$ .

( [link] ) Use the distributive property to compute the product: $\text{60}\cdot \text{46}$ .

$\text{60}\left(\text{50}-4\right)=3,\text{000}-\text{240}=2,\text{760}$

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