Lesson 7Dividing Whole Numbers

Division is the opposite of multiplication. In mathematical terms, we say that division is the inverse of multiplication.

If 3 x 2 = 6 then: 6 ÷ 3 = 2 and 6 ÷ 2 = 3

Topic 1
Introduction to Dividing Whole Numbers

Definitions

 The number being divided is called the dividend. The number doing the dividing is called the divisor. The result of the division called the quotient. The division sign ( ÷ ) indicates the division operation.

Sometimes you will find division problems expressed in the vertical form ...

... and quite often in the division box form:

NOTES

In this lesson, you will not be required to divide a whole number by one that has a  larger value. In other words, you will not see a problem such as 8 ÷ 16. This is a valid problem, but the quotient is a fraction, and fractions do not belong to the whole-number system

 Any value divided by one is equal to the original value. Example: 5  ÷ 1 = 5 Zero divided by any whole number (except 0) is zero. Example:  0 ÷  2 = 0

Topic 2
Division with Remainders

Most combinations of whole numbers do not divide evenly. In other words, their quotient cannot be expressed as a simple whole number.
• 2 divides evenly into 6:  2 ) 6   = 3
• 7 does not divide evenly into 37:  7 ) 37   =  ?
7 divides into 37 five times ... with a remainder of 2

 Procedure When whole numbers do not divide evenly: Find the largest number of times the divisor will divide into the dividend.  This is the quotient. To determine the remainder, multiply the quotient by the divisor, then subtract the result from the dividend.

Whole-number division  isn't a common practice in real  life, so you might have forgotten all about them. Take some time to refresh your memory:

Division with remainders

Topic 2
"Long" Division

 Note Yes, it is the popular opinion that there is no real need to put so much effort into solving long-division problems when you have calculators that can do all the monotonous work for you. The trend in education and the workplace is away from the need for button pushers and toward people who understand fundamental principles and know how to use them to solve problems as we've never faced before -- even if the work is sometimes dreary..

Examples of Long Division

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

Use long division to solve these examples. Keep working them until you have completely mastered the process.



 If would like to see more examples or work on a wider range of exercises, you can go to a more detailed tutorial .