Back
Introduction to Multiplication
> ... Math > 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 $$2 \times 3$$.
$$2 + 2 + 2 = 2 \times 3 = 6$$

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.

×12345678910
112345678910
22468101214161820
336912151821242730
4481216202428323640
55101520253035404550
66121824303642485460
77142128354249566370
88162432404856647280
99182736455463728190
10102030405060708090100

### Multiplication Resources

IXL: Multiplication facts to 12
Education: Multiplication Table Worksheet

Introduction to multiplication
Multiplication of 0, 1, and 10

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

Multiplication of 0
Any number multiplied by 0 equals 0.

• $$3 \times 0 = 0$$
• $$84 \times 0 = 0$$
• $$1538976 \times 0 = 0$$

Multiplication of 1
Any number multiplied by 1 remains the same number.

• $$5 \times 1 = 5$$
• $$99 \times 1 = 99$$
• $$53702 \times 1 = 53702$$

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

• $$5 \times 10 = 50$$
• $$44 \times 10 = 440$$
• $$19875 \times 10 = 198750$$

In other words, multiplying by 10 moves all the numbers one place value to the left, or one place value higher.

### Practice Problems

Evaluate the following expression:
1. $$1 × 4 = ?$$ (
Video Solution
Solution: 4
Details:

(Video Source | Transcript)
)
2. $$4 × 3 = ?$$ (
Solution
Solution: 12
Details:

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.

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 $$3 × 4 = 12$$.
)
3. $$8 × 4 = ?$$ (
Video Solution
Solution: 32
Details:

(Video Source | Transcript)
)
4. $$9 × 8 = ?$$ (
Solution
Solution: 72
Details:
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 $$9 × 8 = 8 × 9 = 72$$.
)
5. $$0 × 65 = ?$$ (
Solution
Solution:
0
)
6. $$84 × 1 = ?$$ (
Solution
Solution:
84
)
7. $$49 × 10 = ?$$ (
Solution
Solution:
490
)

## Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.