Introduction
Your grade level gets a party at the end of the year!
There are 20 students in each class and there are 8 classes.
At the party each student will get to eat a burger.
The principal wants to figure out how many burgers she will need to order.
To find the number, she will multiply 20 by 8.
We could have figured out the number of burgers we needed to buy by adding, but multiplying is much faster.
This lesson will take you through the basics of multiplying whole numbers together.
Multiplying Whole Numbers Using Long Multiplication
The first method for multiplying numbers together is long multiplication. This method allows us to solve for the multiplication of large numbers by multiplying smaller ones together.
Our process for long multiplication can be broken into the following steps:
Step 1  Line up both numbers we are multiplying above each other with the correct units places above one another (ones above ones, tens above tens, etc.)
Step 2  Multiply each digit by each other.
Occasionally, we will have to carry a digit to the next units place if our result is more than one digit when we multiply.
When we begin multiplying by the next unit place, we will have to cross out a unit space where we record our answer.
Step 3  Add together the result of our multiplication.
Let's take a look at the process in action.
Multiplying Whole Numbers by Long Multiplication
We want to multiply 36 by 24.
Our first step is to line up the correct units spaces above each other.
Start with the rightmost digit of our bottom number. Begin by multiplying it with the number directly above it.
4 × 6 = 24
Since our result is greater than one digit, we will record the first digit below our multiplication and carry the 2 to the next units place.
We will add this extra number after our next multiplication.
Continue multiplying the first digit of the bottom number by the next digit in the top number.
4 × 3 = 12
Before we record the 12, we need to add the 2 that we carried over from our previous step.
12 + 2 = 14
Now that we are done multiplying with our first digit, we will move on to the next one. It is important to write a zero or to cross out a unit place, and begin recording our result one unit to the left. We do this since we are multiplying the tens unit place now.
2 × 6 = 12
Since this is more than one digit, we will record the 2 and carry the 1 to our next unit space.
Continue multiplying until we are done with our digits on top.
2 × 3 = 6
Don't forget to add the 1 to the result of our multiplication.
6 + 1 = 7
After multiplying our digits together, we need to add up our result.
Our final answer is that:
24 × 36 = 864
Regardless of the number of digits we are multiplying by, this process will work if we set it up correctly.
Let's take a look at a slightly more difficult problem.
Multiplying Whole Numbers by Long Multiplication
The more digits we add, the more difficult our problems will get.
Our first step remains the same, we have to line up the correct units spaces above each other.
Let's solve 216 × 14.
Begin with the first digit of the smaller number and multiply by the first digit of the top number.
4 × 6 = 24
Since our result is a two digit number we will carry the 2 to the next units place and add it later.
Continue multiplying each of the other digits by 4. The result should be 904.
We will now move on to the next digit of our bottom number and multiply it by each of our digits on top.
Always cross out a unit space when we shift to the next digit like this.
This is the result after multiplying each of our digits by 1.
To get our final answer, we need to add up the result of our multiplication.
Our final answer is that:
216 × 14 = 3064
Muliplying Whole Numbers Using Area Models
Another way we can find the value of multiplication problems is by the use of area models.
This method can be broken down into the following steps:
Step 1  Split a rectangle up into as many pieces as the first number in our multiplication.
Step 2  Split the rectangle from the first step again into as many pieces as the second number.
Multiplying Whole Numbers Using Area Models
Let's take a look at multiplying 6 by 4 using a rectangular area model.
Our first step is to split a rectangle into 6 pieces.
We will then split the rectangle from earlier into 4 pieces. The number of individual rectangles is equal to the result of our multiplication.
If you count the individual rectangles, we will have 24 total rectangles.
This tells us that 6 times 4 is equal to 24.
Although this method may seem easier to use, for problems involving large numbers it would take too long for us to count each individual square and we may make mistakes.
For this reason, long multiplication is a more reliable method in general.

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