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Learning to Divide |
What is division? Division is the opposite of multiplication. As an example, if you have 6 pencils to give out to 3 students, how many pencils will each student get? To solve this, we need to divide the 6 pencils into 3 equal groups. There are three common symbols to use for division: "/ ", "÷", and "—". For example, dividing the 6 pencils into 3 groups can be written in either of the following three ways:
6/3
6 ÷ 3
6
3All these symbols are very commonly used so make sure that you remember them. In this lesson we will use the first symbol, which is 6/3. In all the above cases, the number 6 is called the dividend and the number 3 is called the divisor. The answer is called the quotient.
dividend / divisor = quotient
Another name that is used for the 6 is numerator and for the 3 is denominator.
numerator
denominator= quotient We will use integer bars to solve this problem. First we start with a size 6 or dark green bar that needs to be divided into 3 equal pieces:
Then we have to find 3 equal bars that make up a train that matches exactly the size 6 bar. In this case, the size 2 or red bars are the ones that work. Here is the red train:
Since the bars that work turn out to be the red bars, that means that the answer is 2 which is the size of the red bar. Here is the equation for the same problem:
6 / 3 = 2
6 divided by 3 equals 2.
Since division is really the opposite of multiplication, if 6 divided by 3 equals 2, then 3 multiplied by 2 equals 6. Can you guess what 6 divide by 2 would be? Or 6/2 = ?
Now you need a train that has two equal bars that add up to 6. The bars that make up this train would be the size 3 or light green bars. Therefore,
6 / 2 = 3
Notice that if 6 / 3 = 2 then 6 / 2 = 3.
Dividing bars into equal parts - Some bars can't be divided into two equal bars. This would include all of the odd sized bars such as the white, green, yellow, black and blue bars. Other bars can't be divided into three equal bars such as the white, red, purple, yellow, black, brown, and orange bars. Some bars can not be divided by 4 or 5, etc.
Remainder - We will introduce the concept of what a remainder is when doing division. Let's divide 9 pencils among 4 students. We need to build a train made out of 4 bars to add up to 9. Here is our try:
As you can see, the light green bars are too long and the red bars are too short leaving an empty space. To build a train that adds up to 9 using 4 equal bars, we used 4 red bars and ended up with size 1 leftover or space to complete the 9. The size 1 bar that completes the train is called the remainder.
So dividing 9 pencils among 4 students, each student gets 2 pencils and we have 1 pencil left over. As an equation this would be written:
9 / 4 = 2 with a remainder of 1
Exercises - Solve the following equations. Watch out, because some of them may have remainders.
8 / 2 = 15 / 3 = 12 / 4 = 7 / 3 = 15 / 4 = 16 / 4 = 14 / 3 = 25 / 5 =
<- Click on this image to start the applet
When you have solved all the equations, check your answers.
Factors - If there is no remainder when you divide, then the divisor or denominator and the quotient are factors of the dividend or numerator. For example in the following equation,
12 / 4 = 3
4 and 3 are the factors of 12.
The Role of Zero in Division - Zero plays an important role in division both as a numerator or denominator.
When numerator is 0 - If you have 0 pencils to give out to 7 students, how many pencils will each student get? Think, think, think ...
Each student would get 0 pencils. The equation would look like:
0 / 7 = 0
Whenever the numerator is 0 the result is always 0.
When the denominator is 0 - If you have 7 pencils to give out to 0 students, how many pencils will be distributed? Think, think, think ... It can't be done. This is invalid. Dividing by 0 should never be done. There is no valid answer when dividing by 0.
7 / 0 = [ invalid ]
Learning More About Multiplication Using Integer Bars
Table of Contents
Learning About Fractions Using Integer Bars
Last Updated: Wednesday, 16-Jul-2003 01:06:06 GMT
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