WHOLE NUMBER MULTIPLICATION

Concept: Use multiplication when you need to add the same number many times. The answer to a multiplication problem is called the product.

Use the Multiplication Table below for help with simple multiplication problems. Follow the Steps for Using the Multiplication Table listed below.

For help with more complicated multiplication problems, follow the Steps for Multiplication with Multiple Digit Numbers listed below.

Multiplication Table

X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24
3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36
4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48
5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60
6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72
7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84
8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96
9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108
10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120
11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132
12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144

Steps for Using the Multiplication Table

Step 1 | Select the number in the top row that you wish to multiply.
Step 2 | Select the number in the far left column that you wish to multiply by.
Step 3 | Scan to the right of the number you selected in Step 2 until you are directly below the number you selected in Step 1. There you will find the product of the two numbers you selected.

Example Multiply 5 by 5

Step 1 | Select the number in the top row that you wish to multiply. | 5
Step 2 | Select the number in the far left column by which you wish to multiply. | 5
Step 3 | Scan to the right of the number you selected in Step 2 until you are directly below the number you selected in Step 1. There you will find the product of the two numbers you selected. | 25

Steps for Multiplication of Multiple Digit Numbers

Step 1 | Arrange the numbers being multiplied so that digits with the same place value are aligned.
Step 2 | Multiply all the digits in the top number by the digit in the ones column (furthest to the right) of the bottom number, working from right to left. Place this partial product below the Results Line. (If the product in any column is greater than 9, place the right-most digit of the product below the Results line in the appropriate column, and carry the rest to the top of the next column to the left.)
Step 3 | Next, multiply the digits in the top number by the digit in the tens column of the bottom number. Place this new partial product below the first partial product, with a zero to the right of the second partial product, as a placeholder. For each additional partial product, place an additional zero to the right of the partial product, as a placeholder. Continue this process until all the digits of the top number have been multiplied by all of the digits of the bottom number.
Step 4 | Finally, add the partial products (including the zeros you have added as placeholders) to find the product of the equation.

Example Multiply 913 by 52

Step 1 | Arrange the numbers being multiplied so that digits with the same place value are aligned. | 9 1 3 5 2
Step 2 | Multiply the digits in the top number by the digit in the ones column (furthest to the right) of the bottom number (2), working from right to left. Place this partial product below the Results Line. | 913 X 5 2 1,826
Step 3 | Next, multiply the digits in the top number by the digit in the tens column of the bottom number. Place a zero in the ones column as a placeholder, and then place this new partial product below the first partial product. (For each additional partial product, add an additional zero. Continue this process until the top number has been multiplied by all of the digits of the bottom number. In the current example there are only two digits in the bottom number, so we are finished with this step now.) | 1 913 X 5 2 1,826 +45,65 0
(NOTE) | The following rule from Step 2 applies here. (If the product in any column is greater than 9, place the right-most digit of the product below the Results line in the appropriate column, and carry the rest to the top of the next column to the left.) 5 (from 52) times 3 (from 913) equals 15. Place the 5 from the partial product 15 under the tens column, and carry the 1. |
Step 4 | Line up the last digit (furthest to the right) of each partial product under the digit by which you multiplied. This should already be accomplished, if you have been adding zeros as placeholders. | 1 913 X 52 1,82 6 45,6 5 0
Step 4 | Add the partial products together to find the product of the equation. | 913 X 52 1,826 + 45,650 47,476