Open Textbook Adoptions- Addition
- Addition Visualized on the Number Line
- The Addition Process
- Addition Involving Carrying
- Calculators
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(What does "Endorsed by" mean?)Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to add whole numbers. By the end of this module, students should be able to understand the addition process, add whole numbers, and use the calculator to add one whole number to another.
Suppose we have two collections of objects that we combine together to form a third collection. For example,
We are combining a collection of four objects with a collection of three objects to obtain a collection of seven objects.
The process of combining two or more objects (real or intuitive) to form a third, the total, is called addition.
In addition, the numbers being added are called addends or terms, and the total is called the sum. The plus symbol (+) is used to indicate addition, and the equal symbol (=) is used to represent the word "equal." For example,
Addition is easily visualized on the number line. Let's visualize the addition of 4 and 3 using the number line.
To find
Thus,
We'll study the process of addition by considering the sum of 25 and 43.
We write this as 68.
We can suggest the following procedure for adding whole numbers using this example.
To add whole numbers,
The process:
Add 276 and 103.
Add 1459 and 130
In each of these examples, each individual sum does not exceed 9. We will examine individual sums that exceed 9 in the next section.
Perform each addition. Show the expanded form in problems 1 and 2.
Add 63 and 25.
88
Add 4,026 and 1,501.
5,527
Add 231,045 and 36,121.
267,166
It often happens in addition that the sum of the digits in a column will exceed 9. This happens when we add 18 and 34. We show this in expanded form as follows.
Notice that when we add the 8 ones to the 4 ones we get 12 ones. We then convert the 12 ones to 1 ten and 2 ones. In vertical addition, we show this conversion by carrying the ten to the tens column. We write a 1 at the top of the tens column to indicate the carry. This same example is shown in a shorter form as follows:
Perform the following additions. Use the process of carrying when needed.
Add 1875 and 358.
The sum is 2233.
Add 89,208 and 4,946.
The sum is 94,154.
Add 38 and 95.
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.
The sum is 4,868.
Numbers other than 1 can be carried as illustrated in Example 8.
Find the sum of the following numbers.
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.
Perform each addition. For the next three problems, show the expanded form.
Add 58 and 29.
87
Add 476 and 85.
561
Add 27 and 88.
115
Add 67,898 and 85,627.
153,525
For the next three problems, find the sums.
167
2,468
434,826
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).
Use a calculator to find each sum.
|
|
Display Reads | |
| Type | 34 | 34 |
| Press | + | 34 |
| Type | 21 | 21 |
| Press | = | 55 |
The sum is 55.
|
|
Display Reads | ||
| Type | 106 | 106 | The calculator keeps a running subtotal |
| Press | + | 106 | |
| Type | 85 | 85 | |
| Press | = | 191 | ←
|
| Type | 322 | 322 | |
| Press | + | 513 | ←
|
| Type | 406 | 406 | |
| Press | = | 919 | ←
|
The sum is 919.
Use a calculator to find the following sums.
155
19,750
30,682
For the following problems, perform the additions. If you can, check each sum with a calculator.
19
48
98
978
368
12,777
58,738
45,169,739
33
81
91
809
862
2,321
1,141,204
562,364,111
942,302,364,207,060
234
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
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
((Reference)) Each period of numbers has its own name. From right to left, what is the name of the fourth period?
((Reference)) In the number 610,467, how many thousands are there?
0
((Reference)) Write 8,840 as you would read it.
((Reference)) Round 6,842 to the nearest hundred.
6,800
((Reference)) Round 431,046 to the nearest million.
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This work is licensed by Denny Burzynski and Wade Ellis under a Creative Commons Attribution License (CC-BY 3.0), and is an Open Educational Resource.
Last edited by Collins Williamson on Aug 18, 2010 8:10 pm -0500.
"Used as supplemental materials for developmental math courses."