SECTION 1-WHOLE NUMBER ARITHMETIC

ARITHMETIC INTRODUCTION

We'll start with a brief review of arithmetic with whole numbers.
You should have no trouble adding, subtracting, multiplying, and dividing single digit numbers. If you need help with adding, subtracting, multiplying or dividing single digit numbers go to the appendix. There you will find the addition and multiplication tables, as well as sections on subtraction and division.

Before we begin, let me take a minute to discuss two, three, and four digit numbers.

Any two digit number can be thought of a combination of a specific number of tens and a specific number of ones.
The digit in the far right hand column is in what is commonly called the "ones column." It refers to the number of ones needed to make up that particular number.
The digit residing immediately to the left of the "ones column" is sitting in what is commonly called the "tens column." It refers to the number of tens needed to make up that particular number.
Here are a few examples illusatrating this concept.
- 12 = 10 + 2 = 1-ten + 2-ones
- 53 = 50 + 3 = 5-tens + 3-ones
- 44 = 40 + 4 = 4-tens + 4-ones
Any three digit number can be thought of a combination of a specific number of hundreds, a specific number of tens, and a specific number of ones.
The digit in the far right hand column is in what is commonly called the "ones column." It refers to the number of ones needed to make up that particular number.
The digit residing immediately to the left of the "ones column" is sitting in what is commonly called the "tens column." It refers to the number of tens needed to make up that particular number.
The digit residing immediately to the left of the "tens column" is sitting in what is commonly called the "hundreds column." It refers to the number of hundreds needed to make up that particular number.
Here are a few examples illusatrating this concept.
- 312 = 300 + 10 + 2 = 3-hundreds + 1-ten + 2-ones
- 553 = 500 + 50 + 3 = 5-hundreds + 5-tens + 3-ones
- 144 = 100 + 40 + 4 = 1-hundred + 4-tens + 4-ones
Any four digit number can be thought of a combination of a specific number of thousands, a specific number of hundreds, a specific number of tens, and a specific number of ones.
The digit in the far right hand column is in what is commonly called the "ones column." It refers to the number of ones needed to make up that particular number.
The digit residing immediately to the left of the "ones column" is sitting in what is commonly called the "tens column." It refers to the number of tens needed to make up that particular number.
The digit residing immediately to the left of the "tens column" is sitting in what is commonly called the "hundreds column." It refers to the number of hundreds needed to make up that particular number.
The digit residing immediately to the left of the "hundreds column" is sitting in what is commonly called the "thousands column." It refers to the number of thousands needed to make up that particular number.
Here are a few examples illusatrating this concept.
- 1312 = 1000 + 300 + 10 + 2 = 1-thousand + 3-hundreds + 1-ten + 2-ones
- 2553 = 2000 + 500 + 50 + 3 = 2-thousands + 5-hundreds + 5-tens + 3-ones
- 5144 = 5000 + 100 + 40 + 4 = 5- thousands + 1-hundred + 4-tens + 4-ones

Now that we understand the makeup of numbers and the addition and multiplication tables, we can start learning arithmetic. Here I'll show you through examples of long addition, subtraction, multiplication, and division. Numbers that are being "carried" will appear in blue.

After each section there will be a series of exercises. In each exercise you'll be asked to work out a problem. place your answer into a text box, and then click on the button marked "Check my answer." You'll then be told whether your answer is correct or not, and be given further options if warranted.

ADDITION

Addition is the process of combining two (or more) like quantities in order to determine the total amount of that quantity. Thus if you had 4 CD's and then you were given 6 more CD's, altogether you would have 4 + 6 or 10 CD's.

In this section I will show you how to add two (or more) digit numbers.
Note: I assume that you can add single digit numbers. If you need help with adding single digit numbers go to the appendix.

The most important things to remember in long addition is lining up your numbers (yes, neatness counts).
Take it one column at a time, starting on the right and working your way to the left. Add the numbers in the column you are working on. If the result is less than 10 then record it directly under the numbers you were adding. If the total is larger than ten the seperate it into the required number of ones and the required number of tens. Record the "ones-value" directly under the numbers that you were adding, and carry the "tens-value" to the column to the left. This "carried digit" will then be added to the rest of the numbers in that column. Continue this process until you reach the last column (i.e. the column furthest to the left). At that point do not bother seperating the ones-values from the tens-value. Simply record the result obtained by adding the digits in that column plus any "carried digits."
Below you'll find some examples illustrating this process.

Addition example 1

54 + 86

First line up the two numbers as shown:
                        54
                      + 86
Now look at the first column.
You have 4 + 6.
4+6=10
10 = 1-ten + 0-ones.
So write the 0 directly underneath the 6 and "carry" the 1 .

1 54 + 86 0

Moving on to the next column we have 5 + 8 + "our carried 1."
5+8+1=14
14 = 10 + 4 = 1-ten + 4-ones.
Usually we would record the 4 and carry the 1 onto the next column, but in this case there is no next column. So simply record 14, with the 4 (of 14) directly below the 8 (of 86).

54 + 86 140

514 + 86 = 140

Addition example 2

972 + 156

First line up the two numbers as shown:
                        972
                      + 156
Now look at the first column.
You have 2 + 6.
2+6=8
Write the 8 directly underneath the 6.

972 + 156 8

Moving on to the next column we have 7 + 5.
7 + 5 = 12
12 = 10 + 2 = 1-ten + 2-ones.
Record the 2 and carry the 1 onto the next column.

1 972 + 156 28

Moving on to the next column we have 9 + 1 + "our carried 1."
9+1+1=11
11 = 10 + 1 = 1-ten + 1-one.
Usually we would record the first 1 (the one-value of 11) and carry the second 1 (the ten-value of 11) onto the next column, but in this case there is no next column. So simply record 11.

972 + 156 1128

972 + 156 = 1128

Addition example 3

14,589 + 834

First line up the two numbers as shown:

                      14,589
                      +  834

Now look at the first column.
You have 9 + 4.
9+4=13
Write the 3 directly underneath the 4 and "carry" the 1.

1 14,589 + 834 3

Moving on to the next column we have 8 + 3 + "our carried 1."
8+3+1=12
Write down the two and carry the 1 onto the third column

1 14,589 + 834 23

Now moving on to the third column we have 5 + 8 + "our borrowed 1".
5 + 8 + 1 = 14
Write down 4 and carry 1.

1 14,589 + 834 423

Now moving on we have 4 plus "our carried 1" giving us 5.

14,589 + 834 5,423

Lastly, we have our last column with 1 in it, and nothing else. Just write down the 1

14,589 + 834 15,423

14,589 + 834 = 15,423

Now it's your chance to prove you've been paying attention!

Click on the "generate an additon problem" button to see your exercise. Place your answer in the text box and then click the "check my answer" button. The computer will then tell you whether or not your answer is correct.

After you complete the problem, you can generate another problem by first clicking the "reset button" and then clicking the "generate an addition problem" button. Continue as many times as you wish, and then:

All text, images, and source code c2003 Martin Selditch.