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Add 1875 and 358.

1875 + 358 = 2233. Above the tens, hundreds, and thousands columns are carried ones.

5 + 8 = 13 Write 3, carry 1 ten. 1 + 7 + 5 = 13 Write 3, carry 1 hundred. 1 + 8 + 3 = 12 Write 2, carry 1 thousand. 1 + 1 = 2

The sum is 2233.

Add 89,208 and 4,946.

89,208 + 4,946 = 94,154. Above the tens, thousands, and ten-thousands columns are carried ones.

8 + 6 = 14 Write 4, carry 1 ten. 1 + 0 + 4 = 5 Write the 5 (nothing to carry). 2 + 9 = 11 Write 1, carry one thousand. 1 + 9 + 4 = 14 Write 4, carry one ten thousand. 1 + 8 = 9

The sum is 94,154.

Add 38 and 95.

38 + 95 = 133. Above the tens and the hundreds columns are carried ones.

8 + 5 = 13 Write 3, carry 1 ten. 1 + 3 + 9 = 13 Write 3, carry 1 hundred. 1 + 0 = 1

As you proceed with the addition, it is a good idea to keep in mind what is actually happening.

38 + 95, which is separated into 3 tens + 8 ones over 9 tens + 5 ones. The sum is 12 tens + 13 ones, which is equal to 12 tens + 1 ten + 3 ones, which simplifies to 13 tens + 3 ones, which is equal to 1 hundred + 3 tens + 3 ones, which equals 133.

The sum is 133.

Find the sum 2648, 1359, and 861.

2648 + 1359 + 861 = 4868. Above the tens, hundreds, and thousands columns are carried ones.

8 + 9 + 1 = 18 Write 8, carry 1 ten. 1 + 4 + 5 + 6 = 16 Write 6, carry 1 hundred. 1 + 6 + 3 + 8 = 18 Write 8, carry 1 thousand. 1 + 2 + 1 = 4

The sum is 4,868.

Numbers other than 1 can be carried as illustrated in [link] .

Find the sum of the following numbers.

878016 + 9905 + 38951 + 56817 = 983689. Above the tens column is a carried one. Above the thousands column is a carried 2. Above the ten-thousands column is a carried 3. Above the hundred-thousands column is a carried 1.

6 + 5 + 1 + 7 = 19 Write 9, carry the 1. 1 + 1 + 0 + 5 + 1 = 8 Write 8. 0 + 9 + 9 + 8 = 26 Write 6, carry the 2. 2 + 8 + 9 + 8 + 6 = 33 Write 3, carry the 3. 3 + 7 + 3 + 5 = 18 Write 8, carry the 1. 1 + 8 = 9 Write 9.

The sum is 983,689.

The number of students enrolled at Riemann College in the years 1984, 1985, 1986, and 1987 was 10,406, 9,289, 10,108, and 11,412, respectively. What was the total number of students en­rolled at Riemann College in the years 1985, 1986, and 1987?

We can determine the total number of students enrolled by adding 9,289, 10,108, and 11,412, the number of students enrolled in the years 1985, 1986, and 1987.

9,289 + 10,108 + 11,412 = 30,809. Above the tens, hundreds, and ten-thousands columns are carried ones.

The total number of students enrolled at Riemann College in the years 1985, 1986, and 1987 was 30,809.

Practice set b

Perform each addition. For the next three problems, show the expanded form.

Add 58 and 29.

87

Vertical addition.  5 tens + 8 ones, over 2 tens + 9 ones = 7 tens + 17 ones.

= 7 tens + 1 ten + 7 ones = 8 tens + 7 ones = 87

Add 476 and 85.

561

4 hundreds + 7 tens + 6 ones over 8 tens + 5 ones = 4 hundreds + 15 tens + 11 ones.

= 4 hundreds + 15 tens + 1 ten + 1 one = 4 hundreds + 16 tens + 1 one = 4 hundreds + 1 hundred + 6 tens + 1 one = 5 hundreds + 6 tens + 1 one = 561

Add 27 and 88.

115

Vertical addition. 2 tens + 7 ones, over 8 tens + 8 ones = 10 tens + 15 ones.

= 10 tens + 1 ten + 5 ones = 11 tens + 5 ones = 1 hundred + 1 ten + 5 ones = 115

Add 67,898 and 85,627.

153,525

For the next three problems, find the sums.

57 26   84 ̲

167

847 825   796 ̲

2,468

16,945 8,472 387,721 21,059            629 ̲

434,826

Calculators

Calculators provide a very simple and quick way to find sums of whole numbers. For the two problems in Sample Set C, assume the use of a calculator that does not require the use of an ENTER key (such as many Hewlett-Packard calculators).

Sample set c

Use a calculator to find each sum.

34 + 21 size 12{"34"+"21"} {} Display Reads
Type 34 34
Press + 34
Type 21 21
Press = 55

The sum is 55.

106 + 85 + 322 + 406 size 12{"106"+"85"+"322"+"406"} {} Display Reads
Type 106 106 The calculator keeps a running subtotal
Press + 106
Type 85 85
Press = 191 106 + 85 size 12{"106"+"85"} {}
Type 322 322
Press + 513 191 + 322 size 12{"191"+"322"} {}
Type 406 406
Press = 919 513 + 406 size 12{"513"+"406"} {}

The sum is 919.

Practice set c

Use a calculator to find the following sums.

62 + 81 + 12 size 12{"62"+"81"+"12"} {}

155

9, 261 + 8, 543 + 884 + 1, 062 size 12{9,"261"+8,"543"+"884"+1,"062"} {}

19,750

10 , 221 + 9, 016 + 11 , 445 size 12{"10","221"+0,"016"+"11","445"} {}

30,682

Exercises

For the following problems, perform the additions. If you can, check each sum with a calculator.

14 + 5 size 12{"14"+5} {}

19

12 + 7 size 12{"12"+7} {}

46 + 2 size 12{"46"+2} {}

48

83 + 16 size 12{"83"+"16"} {}

77 + 21 size 12{"77"+"21"} {}

98

321 +   42 ̲

916 +   62 ̲

978

104 + 561 ̲

265 + 103 ̲

368

552 + 237 size 12{"552"+"237"} {}

8, 521 + 4, 256 size 12{8,"521"+4,"256"} {}

12,777

16,408 +   3,101 ̲

16,515 + 42,223 ̲

58,738

616 , 702 + 101 , 161 size 12{"616","702"+"101","161"} {}

43 , 156 , 219 + 2, 013 , 520 size 12{"43","156","219"+2,"013","520"} {}

45,169,739

17 + 6 size 12{"17"+6} {}

25 + 8 size 12{"25"+8} {}

33

84 +   7 ̲

75 +   6 ̲

81

36 + 48 size 12{"36"+"48"} {}

74 + 17 size 12{"74"+"17"} {}

91

486 + 58 size 12{"486"+"58"} {}

743 + 66 size 12{"743"+"66"} {}

809

381 + 88 size 12{"381"+"88"} {}

687 + 175 ̲

862

931 + 853 ̲

1, 428 + 893 size 12{1,"428"+"893"} {}

2,321

12 , 898 + 11 , 925 size 12{"12","898"+"11","925"} {}

631,464 + 509,740 ̲

1,141,204

805,996 +   98,516 ̲

38,428,106 + 522,936,005 ̲

561,364,111

5, 288 , 423 , 100 + 16 , 934 , 785 , 995 size 12{5,"288","423","100"+"16","934","785","995"} {}

98 , 876 , 678 , 521 , 402 + 843 , 425 , 685 , 685 , 658 size 12{"98","876","678","521","402"+"843","425","685","685","658"} {}

942,302,364,207,060

41 + 61 + 85 + 62 size 12{"41"+"61"+"85"+"62"} {}

21 + 85 + 104 + 9 + 15 size 12{"21"+"85"+"104"+9+"15"} {}

234

116 27 110 110 +     8 ̲

75,206 4,152 + 16,007 ̲

95,365

8,226 143 92,015 8 487,553       5,218 ̲

50,006 1,005 100,300 20,008 1,000,009       800,800 ̲

1,972,128

616 42,018 1,687 225 8,623,418 12,506,508 19 2,121       195,643 ̲

For the following problems, perform the additions and round to the nearest hundred.

1,468   2,183 ̲

3,700

928,725      15,685 ̲

82,006   3,019,528 ̲

3,101,500

18,621     5,059 ̲

92   48 ̲

100

16   37 ̲

21   16 ̲

0

11,172 22,749   12,248 ̲

240 280 210   310 ̲

1,000

9,573 101,279   122,581 ̲

For the next five problems, replace the letter m with the whole number that will make the addition true.

62 +     m ̲ 67

5

106 +     m ̲ 113

432 +     m ̲ 451

19

803 +     m ̲ 830

1,893 +       m ̲ 1,981

88

The number of nursing and related care facilities in the United States in 1971 was 22,004. In 1978, the number was 18,722. What was the total num­ber of facilities for both 1971 and 1978?

The number of persons on food stamps in 1975, 1979, and 1980 was 19,179,000, 19,309,000, and 22,023,000, respectively. What was the total number of people on food stamps for the years 1975, 1979, and 1980?

60,511,000

The enrollment in public and nonpublic schools in the years 1965, 1970, 1975, and 1984 was 54,394,000, 59,899,000, 61,063,000, and 55,122,000, respectively. What was the total en­rollment for those years?

The area of New England is 3,618,770 square miles. The area of the Mountain states is 863,563 square miles. The area of the South Atlantic is 278,926 square miles. The area of the Pacific states is 921,392 square miles. What is the total area of these regions?

5,682,651 square miles

In 1960, the IRS received 1,188,000 corporate income tax returns. In 1965, 1,490,000 returns were received. In 1970, 1,747,000 returns were received. In 1972 —1977, 1,890,000; 1,981,000; 2,043,000; 2,100,000; 2,159,000; and 2,329,000 re­turns were received, respectively. What was the total number of corporate tax returns received by the IRS during the years 1960, 1965, 1970, 1972 —1977?

Find the total number of scientists employed in 1974.

A graph entitled employment status of mathematical scientists - 1974. On the graph are histograms with scientific field titles, and a labeled number of the scientists holding the titles. There are 266,000 life scientists, 248,000 physical scientists, 170,000 computer scientists, 217,000 social scientists, 109,000 psychologists, 101,000, mathematicians, and 79,000 environmental scientists.

1,190,000

Find the total number of sales for space vehicle systems for the years 1965-1980.

A graph entitled sales for space vehicle systems, 1965-1980. The histograms for each year are plotted along the horizontal axis, and net sales along the vertical axis. In ascending succession, the sales were 2,449,000,000, 1,956,000,000, 1,725,000,000, 1,656,000,000, 1,562,000,000, 1,751,000,000, 2,119,000,000, 2,002,000,000, 1,870,000,000, 2,324,000,000, 2,539,000,000, and 3,254,000,000.

Find the total baseball attendance for the years 1960-1980.

A graph entitled baseball attendance 1960-1980, with the histograms for each year plotted on the horizontal axis, and the attendance on the vertical axis. In ascending succession, the years had the following attendances, 20,261, 22,806, 29,191, 30,373, 41,402, 44,262, and 43,746.

271,564,000

Find the number of prosecutions of federal officials for 1970-1980.

A graph entitled prosecutions of federal officials 1970-1980, with histograms of the years on the horizontal axis, and number of prosecutions on the vertical axis. The years in ascending succession had the following number of prosecutions, 9, 58, 58, 60, 59, 53, 111, 129, 133, 114, 123.

For the following problems, try to add the numbers mentally.

5 5 3   7 ̲ alignl { stack { size 12{5} {} #size 12{5} {} # size 12{3} {} #size 12{ {underline {7}} } {} } } {}

20

8 2 6    4 ̲ alignl { stack { size 12{8} {} #size 12{2} {} # size 12{6} {} #size 12{ {underline {4}} } {} } } {}

9 1 8 5   2 ̲ alignl { stack { size 12{9} {} #size 12{1} {} # size 12{8} {} #size 12{5} {} # size 12{ {underline {2}} } {}} } {}

25

5 2 5 8 3   7 ̲ alignl { stack { size 12{5} {} #size 12{2} {} # size 12{5} {} #size 12{8} {} # size 12{3} {} #size 12{ {underline {7}} } {} } } {}

6 4 3 1 6 7 9   4 ̲ alignl { stack { size 12{6} {} #size 12{4} {} # size 12{3} {} #size 12{1} {} # size 12{6} {} #size 12{7} {} # size 12{9} {} #size 12{ {underline {4}} } {} } } {}

40

20   30 ̲ alignl { stack { size 12{"20"} {} #size 12{ {underline {"30"}} } {} } } {}

15   35 ̲ alignl { stack { size 12{"15"} {} #size 12{ {underline {"35"}} } {} } } {}

50

16   14 ̲ alignl { stack { size 12{"16"} {} #size 12{ {underline {"14"}} } {} } } {}

23   27 ̲ alignl { stack { size 12{"23"} {} #size 12{ {underline {"27"}} } {} } } {}

50

82   18 ̲ alignl { stack { size 12{"82"} {} #size 12{ {underline {"18"}} } {} } } {}

36   14 ̲ alignl { stack { size 12{"36"} {} #size 12{ {underline {"14"}} } {} } } {}

50

Exercises for review

( [link] ) Each period of numbers has its own name. From right to left, what is the name of the fourth period?

( [link] ) In the number 610,467, how many thousands are there?

0

( [link] ) Write 8,840 as you would read it.

( [link] ) Round 6,842 to the nearest hundred.

6,800

( [link] ) Round 431,046 to the nearest million.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Berger describes sociologists as concerned with
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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