Back To CourseCollege Algebra: Help and Review
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Amy has a master's degree in secondary education and has taught math at a public charter high school.
Okay, so you know about multiplication: that it means to add a number a certain amount of times. You've memorized your multiplication table and you can multiply two small numbers together with ease. For instance, if you were given the problem 3 * 5, you would immediately realize that it means that you are going to add the 3 five times. You might have pictured 5 groups of 3 donuts that you needed to add up. So, you would do 3 + 3 + 3 + 3 + 3. What does this all equal? It equals 15.
And since you've memorized your multiplication table, you didn't need to do all that addition. You just knew it! But what if you need to perform long multiplication, to multiply two larger numbers together, such as 12 * 34? What would you do then? Well, keep watching this video lesson and you will learn a procedure you can use to do just that.
So, let me explain the procedure to you first before showing you. What you will need to know in order to use this procedure is just your knowledge of your basic multiplication, your multiplication skills of small numbers. So, the way this procedure works is you first write your two numbers one on top of the other. And then you begin multiplying the digits by themselves.
You begin by multiplying the last digit of your bottom with your digits of your top number starting from the right and working your way to the left. After you are done multiplying all the digits of your top number, you move on to the next digit of your bottom number. You'll move from right to the left. So now, let me go through an example with you in more detail. This way, you will be able to see what is going on.
So, let's multiply 12 with 34. We first write our numbers one on top of the other. Since we are multiplying, it doesn't matter which number we write on top. It's usually easier to write your smaller number on the bottom. So, we will do just that. We will write 34 on top and 12 on the bottom. We draw a line underneath the last number and put an 'x' to the left of our bottom number to let us know that we are multiplying.
Now, we start our multiplication of our numbers digit by digit. We always move right to left. We start by multiplying the last digit of our bottom number with the digits of our top number, moving from right to left. So, our first multiplication is 2 * 4. It equals 8. We write this 8 underneath the 2. We are moving right to left, so our next multiplication is 2 * 3. What does this equal? It equals 6, so I write the 6 to the left of my 8. So, my first line of my figuring out my answer part is 68.
Now, I'm going to move to the next digit of my bottom number. I am moving right to left, so the digit to the left of the 2 is 1. So, I multiply this number with the digits of my top number, moving right to left. I'm basically repeating what I did with the 2. I multiply my 1 with the 4 first. What is 1 * 4? It is 4. But instead of writing this underneath the 2, I now move one space to the left and write it under the 1. I can put a 0 in line with the 2 to remind me that I don't need a number there.
Now, I've already written something in the space that is directly under the 1, so I write it under that number in line with the 1. Next, I multiply the 1 with the 3. 1 * 3 is 3, so I write this to the left of the 4 to continue my answer for this part. Now that I've multiplied everything together, I draw a line underneath my last line. I am going to add now to find my final answer, so I put a plus sign to the left of my last number. I add 68 + 340. It equals 408. I am now done, and 408 is my answer.
Let's try another one. Let's do 108 * 23. I set up my problem like before. I write 108 on top and 23 on bottom because 23 is the smaller number. I draw a line underneath and put an 'x' to signify that I will be doing multiplication.
Now, I start multiplying my 3 with the digits of my top number. 3 * 8 is 24. Oh wait, this answer has more than one digit. Now what do we do? What we do here is similar to when we add. We write down our last digit, our 4, in our answer area, and then we carry the other digit. So, we write a little 2 on top of the 0 to let us we will be carrying this 2.
Next, we multiply our 3 with the 0. It equals 0, but we have the 2 that we are carrying, so, 0 + 2 = 2. So, we put a 2 in our answer area to the left of our 4. Next, we multiply the 3 with the 1. It equals 3, which we write in our answer area to the left of our 2 now. We are done with this line of our answer.
Next, we move on to multiplying the 2 with the digits of our top number. We move to a new line in our answer area. We put a 0 in our last spot in line with the 3. This tells us that our answer begins one space to the left in line with the 2. So, 2 * 8 = 16. Because this answer is also 2 digits, we write our last digit down in the answer area and carry the 1.
Next, we multiply the 2 with the 0. It equals 0. We carry the 1, so 0 + 1 = 1. We write this 1 in our answer area. Next, we multiply the 2 with the 1. It equals 2, which we write in our answer area. Now, we draw a line underneath our last line and write a plus sign to the left of our bottom number. Now, we add. 324 + 2160 = 2484, which is our final answer, and we are done!
Now, let's review. Multiplication is the adding of a number a certain number of times. Long multiplication is the multiplication of larger numbers. The process of long multiplication involves writing our numbers with the smaller number on the bottom. We then work our way from the right to the left, beginning with the last digit of our bottom number.
We multiply this last digit with the digits of our top number, working from right to left. We then move on to the next digit of our bottom number, going from right to left. We multiply this next number with the digits of our top number, going from right to left again. We write this answer on a new line, starting our answer one space to the left of our last answer. We can write a zero as a placeholder in the space.
If we have more digits in the bottom number, we repeat our process, writing the answer on a new line starting one space to the left of our last answer. We can place zeroes in the empty spaces. Once we've dealt with all the numbers in the bottom number, we add up all our answers to find our final and complete answer.
After finishing this article, you should be able to use long multiplication to solve a multiplication problem.
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Back To CourseCollege Algebra: Help and Review
27 chapters | 228 lessons