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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

are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
In the number 779,844,205 how many ten millions are there?
TELLY Reply
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
Khizar Reply
7hours 36 min - 4hours 50 min
Tanis Reply

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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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