Multiplication

Basic Multiplication Facts

Most multiplication facts fit into a pattern. When you learn these patterns, the rest are easier to memorize.

Counting by 2's: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Counting by 5's: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Squares: 2x2 = 4, 3x3 = 9, 4x4 = 16, 5x5 = 25, 6x6 = 36,

7x7 = 49, 8x8 = 64, 9x9 = 81

There is also a trick to learning 9's, the two digits add up to 9 and are just a little less than the multiple times 10.

10 Remaining math facts to learn:

3x4 = 12, 3 x 6 = 18, 3 x 7 = 21, 3 x 8 = 24,

4x6 = 24, 4x7 = 28, 4x8 = 32,

6x7 = 42, 6x8 = 48, 7x8 = 56

Multiplication by 9

Holding your hands open count from the left the number you want to multiply by 9. In the example above 4 x 9, count to your 4th finger and put it down. The number of fingers on the left (3) is the number of 10's = 30, plus the number of fingers to the right of the one folded down (6). 4 x 9 = 36. This works for 1 x 9.

2 x 9 = 1 ten and 8 = 18.

3 x 9 = 2 tens and 7 = 27,

4 x 9 = 3 tens and 6 = 36,

5 x 9 = 4 tens and 5 = 45,

6 x 9 = 5 tens and 4 = 54,

7 x 9 = 6 tens and 3 = 63,

8 x 9 = 7 tens and 2 = 72 and

9 x 9 = 8 tens and 1 = 81.

Multiplying

two digit numbers

For each digit on the bottom, multiply by every digit on the top. Then add the partial sums.

For example, 47 times 34, start on the right. Multiply the 4 times 7 (= 28), putting the 8 in the ones place and carring the 2. Add the 2 to 4 * 4 (= 16). Write the 6 + 2 in the tens place and carry the 1.

The first partial sum is 188.

Move to the second digit (3). Since it is already in the tens place, but a zero (0) place holder in the ones place. Multiply 3 * 7 (= 21). Write the 1 in the tens place and carry the 2. Add the 2 to 3 * 4 (= 12). Write 2 + 2 in the hundreds place and carry the 1.

The second partial sum is 1410.

Add the two partial sums to get the answer: 47 * 34 = 1598.

Summary

So, by multiplying each single digit on the bottom by every digit on the top, you get a partial sum for each digit in the bottom number. Don't forget to use place holders for the tens place. [You can do the same for 3 digit and 4 digit number multiplication.] Add the partial sums to get the final answer.

Use visual math to check your answers

To visualize 47 x 34, think of 10 * 10 as a square block of 100. If you multiply 40 * 30, you will have 4 * 3 blocks of 100 = 1200. That's one partial sum. There are 2 tens place partial sums to add: 7 * 30 = 210 plus 40 * 4 = 160. Now multiply the ones 7 * 4 = 28.

1200 + 210 + 160 + 28 = 1598 A different way of doing partial sums confirms our answer. [Note 1200 + 210 = 1410 and 160 + 28 + 188 (see above)]

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