Learning to Multiply

 

 

Multiplication

What is multiplication? Multiplication is repeated addition. As an example, if there are 3 students and each student needs 2 pencils, how many pencils are needed all together? You can add "2 + 2 + 2" and the answer would be 6 pencils. The symbol used for multiplication is "x". This same question would be written as the following equation:

3 x 2 = 6

The way this equation is read is "three times two equals six".

Purpose - To learn and practice multiplication using integer bars.

Activity 1 - We will start with an example of using integer bars to do multiplication. There are different ways to do this and remember that multiplication is repeated addition. Let's start by doing the 3 x 2 multiplication.The easiest way is to stack three of the size 2 or red bars:

As you can see they add up to 6 units. Another method to multiply 3 x 2 is to overlap a size 3 or light green bar with a size 2 or red bar:

And then fill out the empty spaces to complete the rectangle as shown below:

Again you can see that it adds up to 6 units. One other method is to just use the size 1 or white bars and bring in 2, 2 and 2 white bars to make a train that adds up to 6 units. However, if the numbers are big this method is a lot of work.

Commutative - Similar to what you learned about the commutative rule with addition, you can use the same rule with multiplication. You can use two size 3 or light green bars:

The answer is the same, 6. The equation to show the commutative rule with multiplication is:

3 x 2 = 2 x 3

This applies to any two numbers that you multiply.

Multiplying more than two numbers - We are going to show that you can multiply more than two numbers at the same time. Let's do 3 x 4 x 5. What we are going to do is use 3 size 4 or purple bars to make a rectangle.

Next make a train using 5 of these rectangles and add them all up.

If you look at one single row in the picture above, there are five size 4 bars which add up to

4 + 4 + 4 + 4 + 4 = 20

As you can see, you can either add the five 12's or three 20's to get the same result which is 60. If you remember, this is the associative rule that we learned with addition. You can show the associative rule with the equations:

(3 x 4) x 5 = 3 x (4 x 5)

Multiplying by zero - Can you imagine a bar of size 0? Size of 0 means there is really no bar or nothing. When you multiply a number by 0 it means that you want 0 or none of those numbers so the answer will always be 0. For example if you multiply 0 x 5 it means you don't have any size 5 bars. If you multiply 5 x 0 it means you have five non-existing bars.

  Any number multiplied by 0 equals 0.

Exercises - To practice multiplication you will multiply every number from 1 to 10 by every number from 1 to 10 by filling in the table below. For example, in the square where the 3 column and the 2 row meet you will write the answer to 3 x 2 = 6. You can see the 6 in the correct square in the table below. Click here to print out a copy of the table for you to fill in.

Multiplication Table

 
1
2
3
4
5
6
7
8
9
10
1
 
   
 
   
   
 
 
 
 
 
2
 
 
 6
 
 
 
 
   
   
  
3
 
   
 
 
   
 
 
   
 
 
4
 
   
 
 
 
 
 
 
 
 
5
 
 
 
 
 
 
 
 
 
 
6
 
 
 
 
 
 
 
 
 
 
7
 
 
 
 
 
 
 
 
   
 
8
 
   
 
 
 
 
 
 
 
 
9
 
 
 
 
 
 
 
 
 
 
10
 
 
 
 
 
   
 
 
 
   

 

   <- Click on this image to start the applet

After you complete the table you can check your answers.

Factors - Factors are the numbers that are multiplied together to get a specific answer. For example:

5 x 6 = 30

In this case the factors are 5 and 6. There are different sets of factors that will give the same answer. For example:

3 x 10 = 30

The number of factors to come up with the same number can be more than two. For example:

2 x 3 x 5 = 30

Below is a list of all of the different factors to get the answer of 12:

12 x 1 = 12
6 x 2 = 12
4 x 3 = 12
3 x 4 = 12
2 x 6 = 12
1 x 12 = 12

Exercises - You can use the integer bars to help you find all of the factors for exercises below.

  1. Find all of the factors for 15.
  2. Find all of the factors for 24.

   <- Click on this image to start the applet

Click here to check your answers.

Multiples - If you take any two factors and you mutiply them, the answer is a multiple of each of those factors. For example:

5 x 6 = 30

The number 30 is a multiple of 5 and also a multiple of 6.

Using integer bars to come up with a multiple of two factors you need to end up with a perfect rectangle. As an example we will use integer bars to build perfect rectangles to find all of the factors for the multiple 12.

Perfect Rectangle
Number of bars
Factors
12 size 1 bars
12 x 1
6 size 2 bars
6 x 2
4 size 3 bars
4 x 3
3 size 4 bars
3 x 4
2 size 6 bars
2 x 6
1 size 12 bar
1 x 12

These are all the perfect rectangles for the multiple 12.

Exercises -

  1. Find all the perfect rectangles for the multiple 36. This will give you all the factors for 36.
  2. Find all the multiples of 3 between the numbers 1 to 36.

   <- Click on this image to start the applet

Once you finish these exercises, you can check your answers.

 


Learning to Add and Subtract Using Integer Bars
Table of Contents
More About Multiplication

 

Last Updated: Tuesday, 15-Jul-2003 23:46:01 GMT


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