# Multiplication Tips and Tricks

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

### Tip #1

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=___+___+___+___+___=____

### Tip #2

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

 Â Â Â Â Â Â Â Â

4 X 2= 8

 Â Â Â Â Â Â Â Â

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

### Tip #3

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

 Â Â Â

In the area below draw the following problems:

4 X 1= 4

6 X 1= 6

### Tip #4

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.

### Tip #5

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 + 7
Ã—1000 + 900 + 60 + 5
35  ```

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

``` 2000 + 500 + 60 + 7+1000 + 900 + 60 + 5
35
300  ```

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

```  2000 + 500 + 60 + 7
Ã— 1000 + 900 + 60 + 5
35
300
2,500  ```

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

```  2000 + 500 + 60 + 7
Ã— 1000 + 900 + 60 + 5
35
300
2,500
10,000  ```

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 + 7
Ã— 1000 + 900 + 60 + 5
35
300
2,500
10,000
420  ```

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 + 60 + 5
35                  300                2,500
10,000
420
3,600  ```

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 + 60 + 5                    35                   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 + 60 + 5                   35                   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 + 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  `

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 + 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                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                       222  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            +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.