Multiplication is the next step on the way to becoming a math champion.

Multiplication and addition are similar:

With an addition problem like 2 + 2 + 2= 6 we can use multiplication and write the problem as 2 X 3= 6 or think of the problem as: add two, three times.

Likewise, 3 X 2= 6 is the same as 3 + 3= 6 -OR- add three, two times.

Write the following additions as multiplications.

Example:

3 + 3 + 3 = __3__ X __3__ =__9__

2 + 2 + 2 + 2=___X_____=___

5 + 5=____X_____=___

4 + 4 + 4=______X_____=___

Write the following multiplications as additions:

2 X 7=___+___+___+___+___+___+___=_____

3 X 5=___+___+___+___+___=____

These pictures show that one of the first things to know is that multiplication problems, like additions, follow the commutative rule which is that

A X B = B X A.

**2 X 4= 8**

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**4 X 2= 8**

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In the area below, use boxes or circles, and draw each of the following problems showing the commutative rule of multiplication.

2 X 4= 8 and 4 X 2= 8

3 X 4= 12 and 4 X 3= 12

1 X 5= 5 and 5 X 1= 5

Besides the commutative rule, multiplications have a 1 rule, too. The 1 rule is simple, if you multiply a number by 1 the answer is always the number.

So: 1 X 3= 3 and 3 X 1= 3, see? Here’s a picture to help you understand:

**1 X 3= 3**

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In the area below draw the following problems:

4 X 1= 4

6 X 1= 6

Multiplication uses a zero rule, too. The zero rule states that any number multiplied by 0 is still 0. To illustate using what we learned above,

0 X 9= 0+0+0+0+0+0+0+0+0 -or- 0 (zero) nine times! So, A X 0=0

Knowing all of the above now, here is the multiplication table. In the area below, make you own multiplication table. This will help you memorize these problems. Which, if you know the one rule and the commutative rule, are all the problems you’ll need to know.

Use the expanded form of the number to solve large multiplications. To multiply numbers such as 2,567 Ã— 1,965 set it up using the expanded form of the number like this:

2000 + 500 + 60 + 7Ã—1000 + 900 + 60 + 5

Now multiply each of the bottom factors starting on the right side to those on the top. For example, multiply the right column, 7 Ã— 5 = 35. Place the 35 under the 7 and 5 and write the answer, 35, as shown below.

2000 + 500 + 60 +7Ã—1000 + 900 + 60 +535

Now multiply 5 Ã— 60 and write the answer, 300, below the 35 as shown below.

2000 + 500 +60+ 7+1000 + 900 + 60 +355300

Now multiply 5 Ã— 500 and write the answer, 2,500 below the 300 as shown below.

2000 +500+ 60 + 7Ã— 1000 + 900 + 60 +35 30052,500

Yes, now multiply 5 Ã— 2000 and write the answer, 10,000 below the 2,500 as shown below.

2000+ 500 + 60 + 7Ã— 1000 + 900 + 60 +35 300 2,500510,000

Now, move to the left of the 5 to 60 on the bottom row and multiply 60 by the upper number 7 and write the answer, 420 under the 10,000 as shown below. add the numbers under the problem up, starting from the right column and move toward the left as follows.

2000 + 500 + 60 +7Ã— 1000 + 900 +35 300 2,500 10,00060+ 5420

Are you beginning to see a trend here?

Now, multiply 60 Ã— 60 and write the answer, 3,600 as shown below.

2000 + 500 +60+ 7Ã— 1000 + 900 +3560+ 5

300

2,500 10,000 4203,600

O.K., guess what? Multiply 60 Ã— 500 for 30,000 and write the answer below as shown.

2000 +500+ 60 + 7

Ã— 1000 + 900 +3560+ 5

300

2,500

10,000

420

3,600

30,000

With that out of the way, multiply 60 Ã— 2000 and write the answer 120,000 below as shown.

2000+ 500 + 60 + 7Ã— 1000 + 900 +3560+ 5

300

2,500

10,000

420

3,600

30,000

120,000

At this time, move left, from the 60 to 900 on the bottom row and multiply that by the upper row 7 and write the answer 630 as shown below.

2000 + 500 + 60 +7Ã— 1000 +900+ 60 + 5

35

300

2,500

10,000

420

3,600

30,000

120,000

6,300

Now multiply 900 Ã— 60 and write the answer, 5,4000, as shown.

2000 + 500 +60+ 7

Ã— 1000 +900+ 60 + 5

35

300

2,500

10,000

420

3,600

30,000

120,000

6,300

54,000

Now multiply 900 Ã— 500 and write the answer, 450,000, as shown.

2000 +500+ 60 + 7

Ã— 1000 +900+ 60 + 5

35

300

2,500

10,000

420

3,600

30,000

120,000

6,300

54,000

450,000

Now multiply 900 Ã— 2000 and write the answer, 1,800,000, as shown.

2000+ 500 + 60 + 7

Ã— 1000 +900+ 60 + 5

35

300

2,500

10,000

420

3,600

30,000

120,000

6,300

54,000

450,000

1,800,000

For the next step, move to the next multiple 1,000 on the bottom row and begin the multiplication process again going from right to left. Now multiply 1000 Ã— 7 and write the answer, 7,000, as shown.

2000 + 500 + 60 +7Ã—1000+ 900 + 60 + 5

35

300

2,500

10,000

420

3,600

30,000

120,000

6,300

54,000

450,000

1,800,000

7,000

Now multiply 1,000 on the bottom row with 60 on the top row and write the answer, 60,000 as shown below.

2000 + 500 +60+ 7

Ã—1000+ 900 + 60 + 5

35

300

2,500

10,000

420

3,600

30,000

120,000

6,300

54,000

450,000

1,800,000

7,000

60,000

Now multiply 1,000 on the bottom row with 500 on the top row and write the answer, 500,000 as shown below.

2000 +500+ 60 + 7Ã—1000+ 900 + 60 + 5

35

300

2,500

10,000

420

3,600

30,000

120,000

6,300

54,000

450,000

1,800,000

7,000

60,000

500,000

For the next step, multiply 1,000 on the bottom row with 2,000 on the top row and write the answer, 2,000,000, as shown below.

2000+ 500 + 60 + 7

Ã—1000+ 900 + 60 + 5

22235

300

2,500

10,000

420

3,600

30,000

120,000

6,300

54,000

450,000

1,800,000

7,000

60,000

500,000

+2,000,000

5,044,155

Finally, add all the numbers on the bottom, starting from the right (ones) column and work toward the left (millions) column. This looks difficult, but you’re adding mostly zeros so it’s really an easy addition. It may help to draw lines between each place value column when adding. With a little practice this is a great way to multiply big numbers. If you use this method for other problems like four-digit times two-digit numbers, always place the larger number above the smaller one.