# 7.1 Whole numbers: addition  (Page 2/2)

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$\begin{array}{ccc}5+8=13\hfill & & \text{Write 3, carry 1 ten.}\hfill \\ 1+7+5=13\hfill & & \text{Write 3, carry 1 hundred.}\hfill \\ 1+8+3=12\hfill & & \text{Write 2, carry 1 thousand.}\hfill \\ 1+1=2\hfill & & \hfill \end{array}$

The sum is 2233.

$\begin{array}{ccc}8+6=14\hfill & & \text{Write 4, carry 1 ten.}\hfill \\ 1+0+4=5\hfill & & \text{Write the 5 (nothing to carry).}\hfill \\ 2+9=11\hfill & & \text{Write 1, carry one thousand.}\hfill \\ 1+9+4=14\hfill & & \text{Write 4, carry one ten thousand.}\hfill \\ 1+8=9\hfill & & \hfill \end{array}$

The sum is 94,154.

$\begin{array}{ccc}8+5=13\hfill & & \text{Write 3, carry 1 ten.}\hfill \\ 1+3+9=13\hfill & & \text{Write 3, carry 1 hundred.}\hfill \\ 1+0=1\hfill & & \hfill \end{array}$

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

The sum is 133.

Find the sum 2648, 1359, and 861.

$\begin{array}{ccc}8+9+1=18\hfill & & \text{Write 8, carry 1 ten.}\hfill \\ 1+4+5+6=16\hfill & & \text{Write 6, carry 1 hundred.}\hfill \\ 1+6+3+8=18\hfill & & \text{Write 8, carry 1 thousand.}\hfill \\ 1+2+1=4\hfill & & \hfill \end{array}$

The sum is 4,868.

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

Find the sum of the following numbers.

$\begin{array}{ccc}6+5+1+7=19\hfill & & \text{Write 9, carry the 1.}\hfill \\ 1+1+0+5+1=8\hfill & & \text{Write 8.}\hfill \\ 0+9+9+8=26\hfill & & \text{Write 6, carry the 2.}\hfill \\ 2+8+9+8+6=33\hfill & & \text{Write 3, carry the 3.}\hfill \\ 3+7+3+5=18\hfill & & \text{Write 8, carry the 1.}\hfill \\ 1+8=9\hfill & & \text{Write 9.}\hfill \end{array}$

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.

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.

87

$\begin{array}{c}=7\phantom{\rule{2px}{0ex}}\text{tens}+1\phantom{\rule{2px}{0ex}}\text{ten}+7\phantom{\rule{2px}{0ex}}\text{ones}\hfill \\ =8\phantom{\rule{2px}{0ex}}\text{tens}+7\phantom{\rule{2px}{0ex}}\text{ones}\hfill \\ =87\hfill \end{array}$

561

$\begin{array}{c}\hfill \text{= 4 hundreds + 15 tens + 1 ten + 1 one}\\ \hfill \text{= 4 hundreds + 16 tens + 1 one}\\ \hfill \text{= 4 hundreds + 1 hundred + 6 tens + 1 one}\\ \hfill \text{= 5 hundreds + 6 tens + 1 one}\\ \hfill =561\end{array}$

115

$\begin{array}{c}\text{= 10 tens + 1 ten + 5 ones}\hfill \\ \text{= 11 tens + 5 ones}\hfill \\ \text{= 1 hundred + 1 ten + 5 ones}\hfill \\ =115\hfill \end{array}$

153,525

For the next three problems, find the sums.

167

2,468

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.

 $\text{34}+\text{21}$ Display Reads Type 34 34 Press + 34 Type 21 21 Press = 55

The sum is 55.

 $\text{106}+\text{85}+\text{322}+\text{406}$ Display Reads Type 106 106 The calculator keeps a running subtotal Press + 106 Type 85 85 Press = 191 ← $\text{106}+\text{85}$ Type 322 322 Press + 513 ← $\text{191}+\text{322}$ Type 406 406 Press = 919 ← $\text{513}+\text{406}$

The sum is 919.

## Practice set c

Use a calculator to find the following sums.

$\text{62}+\text{81}+\text{12}$

155

$9,\text{261}+8,\text{543}+\text{884}+1,\text{062}$

19,750

$\text{10},\text{221}+9,\text{016}+\text{11},\text{445}$

30,682

## Exercises

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

$\text{14}+5$

19

$\text{12}+7$

$\text{46}+2$

48

$\text{83}+\text{16}$

$\text{77}+\text{21}$

98

978

$\begin{array}{c}\hfill 104\\ \hfill \underline{+561}\end{array}$

$\begin{array}{c}\hfill 265\\ \hfill \underline{+103}\end{array}$

368

$\text{552}+\text{237}$

$8,\text{521}+4,\text{256}$

12,777

$\begin{array}{c}\hfill 16,515\\ \hfill \underline{+42,223}\end{array}$

58,738

$\text{616},\text{702}+\text{101},\text{161}$

$\text{43},\text{156},\text{219}+2,\text{013},\text{520}$

45,169,739

$\text{17}+6$

$\text{25}+8$

33

81

$\text{36}+\text{48}$

$\text{74}+\text{17}$

91

$\text{486}+\text{58}$

$\text{743}+\text{66}$

809

$\text{381}+\text{88}$

$\begin{array}{c}\hfill 687\\ \hfill \underline{+175}\end{array}$

862

$\begin{array}{c}\hfill 931\\ \hfill \underline{+853}\end{array}$

$1,\text{428}+\text{893}$

2,321

$\text{12},\text{898}+\text{11},\text{925}$

$\begin{array}{c}\hfill 631,464\\ \hfill \underline{+509,740}\end{array}$

1,141,204

$\begin{array}{c}\hfill 38,428,106\\ \hfill \underline{+522,936,005}\end{array}$

561,364,111

$5,\text{288},\text{423},\text{100}+\text{16},\text{934},\text{785},\text{995}$

$\text{98},\text{876},\text{678},\text{521},\text{402}+\text{843},\text{425},\text{685},\text{685},\text{658}$

942,302,364,207,060

$\text{41}+\text{61}+\text{85}+\text{62}$

$\text{21}+\text{85}+\text{104}+9+\text{15}$

234

$\begin{array}{c}\hfill 75,206\\ \hfill 4,152\\ \hfill \underline{+16,007}\end{array}$

95,365

1,972,128

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

3,700

3,101,500

100

0

1,000

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

5

19

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.

1,190,000

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

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

271,564,000

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

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

20

25

40

50

50

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] ) Round 6,842 to the nearest hundred.

6,800

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

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