Multiplication and Division:

Introduction to Multiplication

In the process of adding the same number over and over again, people discovered an important shortcut. It is called multiplication.

2 + 2 + 2 = 6
Means two is added 3 times, or 2 × 3.
2 + 2 + 2 = 2 × 3 = 6

You can use this multiplication chart to help you learn your multiplication facts. Use it to make flashcards to help you memorize the facts. Memorizing your multiplication facts will be helpful to you and make math easier as you continue through the course.

×	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

Multiplication Resources

IXL: Multiplication facts to 12

Education: Multiplication Table Worksheet

Video Source (05:20 mins) | Transcript

Video Source (01:38 mins) | Transcript

Here are some general rules of multiplication as explained in the video.

Multiplication of 0

Any number multiplied by 0 equals 0.

3 × 0 = 0
84 × 0 = 0
1538976 × 0 = 0

Multiplication of 1

Any number multiplied by 1 remains the same number.

5 × 1 = 5
99 × 1 = 99
53702 × 1 = 53702

Multiplication of 10

Any number multiplied by 10 is the same number but with a new 0 at the end.

5 × 10 = 50
44 × 10 = 440
19875 × 10 = 198750
In other words, multiplying by 10 moves all the numbers one place value to the left, or one place value higher

Additional Resources

Khan Academy: Introduction to Multiplication (03:32 mins, Transcript)
Khan Academy: Multiplication With Arrays (04:18 mins, Transcript)
Khan Academy: Basic Multiplication (13:20 mins, Transcript)

Practice Problems

Evaluate the following expression:

1 × 4 = ?
4 × 3 = ?
8 × 4 = ?
9 × 8 = ?
0 × 65 = ?
84 × 1 = ?
49 × 10 = ?

Solutions

4 (Solution Video | Transcript)
12 (Written Solution)

Start with 4 circles to represent the 4 in our problem.

Each circle is assigned 3 black dots to represent the 3 in our problem.

This grouping represents the multiplication of 4 × 3.

Count the black dots only. This represents the answer to our multiplication problem.

The answer is 12.

Another way to look at this is as rows and columns. Here we have three columns and four rows of circles. In other words, three columns of four circles or four rows of three circles. Either way we look at it, we have 12 total circles. Therefore, 4 × 3 = 12 and 3 × 4 = 12.
32 (Solution Video | Transcript)
72 (Written Solution)

The circles represent the 9 in our multiplication problem.

Each circle now contains 8 images of a smiley face. These represent the 8 in the problem.

Next, remove the 9 large circles. There are 9 groups of 8 smiley faces. Count the smiley faces only.

This is the same as 8 added together 9 times. (It is also the same as 9 added together 8 times.)

This represents the answer to 9 × 8. The total count is 72.

The answer to 9 × 8 is 72.

Another way to look at this is as repeated addition. Nine added together eight times is the same as 9 × 8. Similarly, 8 added together 9 times is 8 × 9. An exciting thing about multiplication is that it is commutative. This means 9 × 8 = 8 × 9 = 72.
0
84
490

×	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

×	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

×	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100