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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

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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