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Practice set b

Perform each operation. Simplify when possible.

Add 4 gal 3 qt to 1 gal 2 qt.

6 gal 1 qt

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Add 9 hr 48 min to 4 hr 26 min.

14 hr 14 min

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Subtract 2 ft 5 in. from 8 ft 7 in.

6 ft 2in.

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Subtract 15 km 460 m from 27 km 800 m.

12 km 340 m

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Subtract 8 min 35 sec from 12 min 10 sec.

3 min 35 sec

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Add 4 yd 2 ft 7 in. to 9 yd 2 ft 8 in.

14 yd 2 ft 3 in

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Subtract 11 min 55 sec from 25 min 8 sec.

13 min 13 sec

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Multiplying a denominate number by a whole number

Let's examine the repeated sum

4 ft 9 in. + 4 ft 9 in. + 4 ft 9 in. 3 times = 12 ft 27 in.

Recalling that multiplication is a description of repeated addition, by the distribu­tive property we have

3 ( 4 ft 9 in . ) = 3 ( 4 ft + 9 in. ) = 3 4 ft + 3 9 in. = 12 ft + 27 in. Now, 27 in. = 2 ft 3 in. = 12 ft + 2 ft + 3 in. = 14 ft + 3 in. = 14 ft 3 in.

From these observations, we can suggest the following rule.

Multiplying a denominate number by a whole number

To multiply a denominate number by a whole number, multiply the number part of each unit by the whole number and affix the unit to this product.

Sample set c

Perform the following multiplications. Simplify if necessary.

6 2 ft 4 in. = 6 2 ft + 6 4 in. = 12 ft + 24 in.

Since 3 ft = 1 yd size 12{"3 ft"=" 1 yd"} {} and 12   in . = 1 ft size 12{"12"" in" "." ="1 ft"} {} ,

12 ft + 24 in. = 4 yd + 2 ft = 4 yd 2 ft

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8 5 hr 21 min 55 sec = 8 5 hr + 8 21 min + 8 55 sec = 40 hr + 168 min + 440sec = 40 hr + 168 min + 7 min + 20 sec = 40 hr + 175 min + 20 sec = 40 hr + 2 hr + 55 min + 20 sec = 42 hr + 55 min + 20 sec = 24hr + 18hr + 55 min + 20 sec = 1 da + 18 hr + 55 min + 20 sec = 1 da 18 hr 55 min 20 sec

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Practice set c

Perform the following multiplications. Simplify.

2 10 min size 12{2 cdot left ("10 min" right )} {}

20 min

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5 3 qt size 12{5 cdot left ("3 qt" right )} {}

15 qt = 3 gal 3 qt size 12{"15 qt"="3 gal 3 qt"} {}

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4 5 ft 8 in . size 12{4 cdot left (5" ft 8 in" "." right )} {}

20 ft 32 in . = 7 yd 1 ft 8 in . size 12{"20 ft 32 in" "." =" 7 yd 1 ft 8 in" "." } {}

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10 2 hr 15 min 40 sec size 12{"10" cdot left (2" hr 15 min 40 sec" right )} {}

20 hr 150 min 400 sec = 22 hr 36 min 40 sec size 12{"20 hr 150 min 400 sec"="22 hr 36 min 40 sec"} {}

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Dividing a denominate number by a whole number

Dividing a denominate number by a whole number

To divide a denominate number by a whole number, divide the number part of each unit by the whole number beginning with the largest unit. Affix the unit to this quotient. Carry any remainder to the next unit.

Sample set d

Perform the following divisions. Simplify if necessary.

12 min 40 sec ÷ 4 size 12{ left ("12 min 40 sec" right ) div 4} {}

Long division. 12 min and 40 sec divided by 4. 4 goes into 12 minutes 3 times, making a quotient of 3 minutes with no remainder. 4 goes into 40 seconds 10 times, making a quotient of 10 seconds with no remainder. The total quotient is 3 min 10 sec.

Thus 12 min 40 sec ÷ 4 = 3 min 10 sec size 12{ left ("12 min 40 sec" right ) div 4=3" min 10 sec"} {}

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5 yd 2 ft 9 in . ÷ 3 size 12{ left ("5 yd 2 ft 9 in" "." right ) div 3} {}

Long division. 5 yd 2 ft 9 in divided by 3. 3 goes into 5 yards one time with a remainder of 2 yards. Bring down the 2 feet. 2 yards and 2 feet is eight feet. 3 goes into eight feet twice with a remainder of 2 feet. Bring down the 9 inches. 2 feet 9 in is equal to 22 inches. 3 goes into 33 inches exactly 11 times. The total quotient is 1 yd 2 ft 11 in. Convert to feet: 2 yd 2 ft = 8 ft . Convert to inches: 2 ft 9 in . = 33 in .

Thus 5 yd 2 ft 9 in . ÷ 3 = 1 yd 2 ft 11 in . size 12{ left ("5 yd 2 ft 9 in" "." right ) div 3=1" yd 2 ft 11 in" "." } {}

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Practice set d

Perform the following divisions. Simplify if necessary.

18 hr 36 min ÷ 9 size 12{ left ("18 hr 36 min" right ) div 9} {}

2 hr 4 min

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34 hr 8 min . ÷ 8 size 12{ left ("34 hr 8 min" "." right ) div 8} {}

4 hr 16 min

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13 yd 7 in . ÷ 5 size 12{ left ("13 yd 7 in" "." right ) div 5} {}

2 yd 1 ft 11 in

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47 gal 2 qt 1 pt ÷ 3 size 12{ left ("47 gal 2 qt 1 pt" right ) div 3} {}

15 gal 3 qt 1 pt

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Exercises

For the following 15 problems, simplify the denominate numbers­.

85 min

1 hour 25 minutes

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26 qt

6 gallons 2 quarts

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135 oz

8 pounds 7 ounces

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16,300 mL

16 liters 300 milliliters (or 1daL 6 L 3dL)

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For the following 15 problems, perform the indicated opera­tions and simplify the answers if possible.

Add 6 min 12 sec to 5 min 15 sec.

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Add 14 da 6 hr to 1 da 5 hr.

15 days 11 hours

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Add 9 gal 3 qt to 2 gal 3 qt.

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Add 16 lb 10 oz to 42 lb 15 oz.

59 pounds 9 ounces

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Subtract 3 gal 1 qt from 8 gal 3 qt.

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Subtract 3 ft 10 in. from 5 ft 8 in.

1 foot 10 inches

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Subtract 5 lb 9 oz from 12 lb 5 oz.

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Subtract 10 hr 10 min from 11 hr 28 min.

1 hour 18 minutes

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Add 3 fl oz 1 tbsp 2 tsp to 5 fl oz 1 tbsp 2 tsp.

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Add 4 da 7 hr 12 min to 1 da 8 hr 53 min.

5 days 16 hours 5 minutes

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Subtract 5 hr 21 sec from 11 hr 2 min 14 sec.

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Subtract 6 T 1,300 lb 10 oz from 8 T 400 lb 10 oz.

1 ton 1,100 pounds (or 1T 1,100 lb)

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Subtract 15 mi 10 in. from 27 mi 800 ft 7 in.

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Subtract 3 wk 5 da 50 min 12 sec from 5 wk 6 da 20 min 5 sec.

2 weeks 23 hours 29 minutes 53 seconds

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Subtract 3 gal 3 qt 1 pt 1 oz from 10 gal 2 qt 2 oz.

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Exercises for review

( [link] ) Find the value: 5 8 2 + 39 64 size 12{ left ( { {5} over {8} } right ) rSup { size 8{2} } + { {"39"} over {"64"} } } {} .

1

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( [link] ) Find the sum: 8 + 6 3 5 size 12{8+6 { {3} over {5} } } {} .

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( [link] ) Convert 2 . 05 1 11 size 12{2 "." "05" { {1} over {"11"} } } {} to a fraction.

2 14 275 size 12{2 { {"14"} over {"275"} } } {}

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( [link] ) An acid solution is composed of 3 parts acid to 7 parts water. How many parts of acid are there in a solution that contains 126 parts water?

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( [link] ) Convert 126 kg to grams.

126,000 g

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Questions & Answers

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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