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Chapter 1—Whole Numbers 1-7 Dividing Whole Numbers
Division is the opposite of multiplication. In mathematical terms, we say that division is the If 3 x 2 = 6 then: 6 ÷ 3 = 2 and 6 ÷ 2 = 3 Introduction to Dividing Whole Numbers
Here is a basic division table. If you compare it with the multiplication table in the previous lesson, you will see that it is identical except for the labels and the way you use it. (Division is, indeed, a turned-around, or inverse, form of multiplication). Study the table carefully, and make sure you can figure out how it works.
Sometimes you will find division problems expressed in the vertical form ... ... and quite often in the division box form: Examples and Exercises
Division With Remainders
Sometimes it is necessary to divide a number into a smaller value, such as: 2 ÷ 7 6 ÷ 9 0 ÷ 2 In the whole number system, remainders come to the rescue.
Examples and Exercises
Using Short Division Short division is a convenient way to solve division problems when the divisor is a fairly small number. Here are some examples of problems where short division works well:
Example 1
Examples and Exercises
Example 2
Examples and Exercises
In all the examples of short division you have been working so far, the first digit in the dividend is larger than the divisor. More often, however, the first digit in the dividend is smaller than the divisor. When this happens, you must try dividing the divisor into the first two digits in the dividend. Example 3 Divide 5 into 360
Examples and Exercises
Also, you will find that most division problems end up with a remainder. Example 4
Example 5
Examples and Exercises
Using Long Division
Example 6
Here is an example that is a bit more complicated and has a remainder term. Example 7
Examples of Long Division - Part 1 Carefully study the details of these examples of long division. Do not quit until you are sure you understand every step in every example you see. Exercises for Long Division - Part 1 Use long division to solve these examples. Keep working them until you have completely mastered the procedure.
Here are some more examples and exercises. They are a bit more complicated than the previous set, but this is exactly the level of work you are expected to do.
Examples of Long Division - Part 2 Carefully study the details of these examples of long division. Do not quit until you are sure you understand every step in every example you see. Exercises for Long Division - Part 2 Use long division to solve these examples. Keep working them until you have completely mastered the process. |
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