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College Algebra: Help and Review27 chapters | 228 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Multiplication, one of the basic operations of math, is important not just in elementary math but also in higher math. Watch this video lesson to learn how you can multiply with ease.

**Multiplication** tells you the number of times to add a certain number. So, if we were multiplying three by five, we can say that the problem is asking us to add the three five times.

In math, the symbol for multiplication is either an x or a dot or an asterisk, like 3 * 5. We can even use parentheses to show multiplication, such as 3(5).

The easiest way to multiply is to visualize your numbers as things. For example, for multiplying 3 * 5, we can think of the three as three toy cars. The five tells us how many groups of toy cars we are going to be adding up. We have five groups of three toy cars. We put them all together and what do we get? We get 15 toy cars, so 3 times 5 is equal to 15.

Now, let's see how we multiply two numbers together. Say we wanted to multiply 6 and 5 together. Our problem will be asking us to find the answer to 6 * 5. We recall that multiplication is just telling us how many groups of the first number to add together. This particular problem is telling us to add the 6 five times. So, we have 6 + 6 + 6 + 6 + 6. What does this equal? Why, it equals 30! So that is our answer. If it helps, picture the 6 as six toy cars and then picture the multiplication by 5 as five groups of six toy cars.

The more you practice multiplying, the easier it will be to multiply. And pretty soon, you will have your basic multiplications memorized. You can even create a chart to help you remember your multiplications. You start by creating your first row of numbers from 1 to 10. The next row begins with a 1, and then you put the result of multiplying your top row numbers with the 1. Your next row begins with a 2, and it will have the result of multiplying your top row numbers with 2. And you keep adding to your chart until you get to 10. Once you have all these multiplications memorized, multiplying gets very easy.

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 |

. . .

10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

I've given you three complete rows. You will need to fill in the rest. Creating your own multiplication chart also helps you to memorize these numbers.

There are two special multiplication circumstances that I want you to be aware of. The first is that anything multiplied by 1 will equal itself. So, 1,418 * 1 will equal 1,418. The second is that anything multiplied by 0 will always be 0. So, 546 * 0 will equal 0. And it doesn't matter where you see the 1 or the 0. If the 1 comes first, the same rule applies. Likewise with the 0.

Now what if your problem was asking us to multiply several numbers together, such as 2 * 3 * 4? What then? We stay calm and we just tackle it piece by piece. We first multiply the first two numbers, our 2 and 3, together. Then we take that answer and multiply it by the next number, the 4. The answer we get after multiplying by the last number will be our final answer.

So, 2 * 3 * 4 becomes 6 * 4, which becomes 24 for our final answer. Likewise, if we were to multiply 4 * 1 * 3 * 2 together, we first multiply the 4 and the 1 together to get 4. Then we multiply this 4 by the 3 to get 12. Then we multiply the 12 by the 2 to get our final answer of 24.

So, what have we learned? We have learned to **multiply**! Whenever you multiply, you are finding the number of times to add a certain number. So, 2 * 3 is telling you to add the 2 three times. A good way to view multiplication is to think of it in terms of things. So, our 2 * 3 can be seen as three groups of two toy cars. If we piled these three groups together, how many toy cars would we have in total? We would have 6, and that is our answer.

For multiplication, it is recommended that you create your own multiplication table that shows you the answer to all the multiplications from 1 * 1 all the way up to 10 * 10. Creating your own will also help you to memorize these answers. If we were to multiply more than two numbers together, we simply tackle it piece by piece. We start by multiplying the first two numbers together. Then we take that answer and multiply it by the next. We keep going until we've multiplied all the numbers together.

After this lesson, you should be able to:

- Explain how to multiply two numbers as well as how to multiply more than two numbers
- Identify the symbols used to indicate multiplication
- Create a multiplication chart that will help you memorize common multiplications

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College Algebra: Help and Review27 chapters | 228 lessons

- What Is a Number Line? 5:16
- Binary and Non-Binary Operations 5:34
- How to Perform Addition: Steps & Examples 4:07
- How to Perform Subtraction: Steps & Examples 3:46
- How to Perform Multiplication: Steps & Examples 5:22
- How to Perform Division: Steps & Examples 3:56
- Performing Long Division with Large Numbers: Steps and Examples 9:12
- Arithmetic Calculations with Signed Numbers 5:21
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