<< Chapter < Page Chapter >> Page >

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Add 67,898 and 85,627.

153,525

Got questions? Get instant answers now!

For the next three problems, find the sums.

847 825   796 ̲

2,468

Got questions? Get instant answers now!

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

434,826

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!
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.

Got questions? Get instant answers now!

Practice set c

Use a calculator to find the following sums.

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

155

Got questions? Get instant answers now!

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

19,750

Got questions? Get instant answers now!

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

30,682

Got questions? Get instant answers now!

Exercises

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

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

19

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

48

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

98

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

12,777

Got questions? Get instant answers now!

16,515 + 42,223 ̲

58,738

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

45,169,739

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

33

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

91

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

809

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2,321

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

631,464 + 509,740 ̲

1,141,204

Got questions? Get instant answers now!

38,428,106 + 522,936,005 ̲

561,364,111

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

234

Got questions? Get instant answers now!

116 27 110 110 +     8 ̲

Got questions? Get instant answers now!

75,206 4,152 + 16,007 ̲

95,365

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

1,972,128

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

1,468   2,183 ̲

3,700

Got questions? Get instant answers now!

928,725      15,685 ̲

Got questions? Get instant answers now!

82,006   3,019,528 ̲

3,101,500

Got questions? Get instant answers now!

11,172 22,749   12,248 ̲

Got questions? Get instant answers now!

240 280 210   310 ̲

1,000

Got questions? Get instant answers now!

9,573 101,279   122,581 ̲

Got questions? Get instant answers now!

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

432 +     m ̲ 451

19

Got questions? Get instant answers now!

1,893 +       m ̲ 1,981

88

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.
Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.
Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

25

Got questions? Get instant answers now!

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}} } {} } } {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

50

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

50

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

50

Got questions? Get instant answers now!

Exercises for review

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

Got questions? Get instant answers now!

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

0

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

6,800

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask