# Multiplication Practice

Multiplication is a fast way of adding several of the same numbers together. For example, 3 + 3 + 3 + 3 = 12 is the same as saying 3 x 4 = 12. Once you have your multiplication tables memorized, multiplying numbers is an easy task!

Tips for learning times tables:

- Make a list of ALL the times tables, 1-12. Spend a lot of time reading these over. Say them out loud so that you can hear them in your head when you see the problem written out.
- Make (or buy) flashcards! This is a great way to test yourself. Write the problem on one side (for example 3 x 3) and the solution on the other side (9). Then, shuffle them up. Test yourself, show yourself the problem, then say the solution out loud or in your head. If you’re right, put it in one pile (this will be the correct pile); if you’re wrong, put it in another pile (this will be the incorrect pile). Once you’ve gone through the flashcards once, go back and re-do the ones in the incorrect pile. Make sure you test yourself until you can get them right on the first try.
- Play Peace! Peace works like the card game "War." Find a normal deck of playing cards, and a friend or family member to play with. Deal out the entire deck evenly among the people playing. Aces will be worth 1, 2-10 are worth the values they have on them, Jacks are worth 11, and Queens are worth 12. Remove the Kings and the Jokers. Each player will then flip over the top two cards from his/her hand. Each player will multiply those numbers together; the person with the higher number wins, and gets to keep the cards. Keep playing; when your hand runs out, take the cards you’ve won, and play with those. The game lasts until one person is out of cards (the other person wins), or until you run out of time (then, the person with the most cards wins). This is a fun way to practice times tables!

Here is a times table for you to practice from. In order to use this, find the two numbers you want to multiply outside of the box (pick one from the top, and one from the left hand side). Then, look at where those two rows meet, and at that meeting point you will see the answer to the problem. For example, for multiplying 3 x 3, you would find 3 at the time, then find 3 on the left, then trace them with your fingers straight across, and down, until they meet at 9.

## Mulitiplication with Two Digit by One Digit Numbers

After you’ve learned your times tables, you’ll be asked to multiply 2-digit numbers by 1-digit numbers. That would look something like this:

In order to complete this problem, you will break it down into three easy steps. They are:

- Multiply the ones digit of the bottom number by the ones digit of the top number. In this problem, you would be multiplying 5 x 5, which equals 25.
- Split up the 25; write the ones digit (5) in the ones column of the answer. Carry the tens digit (2) above the tens digit of the top number (2). This is in red on the diagram.
- Multiply the ones digit of the bottom number (5) by the tens digit of the top number (2). In this case, it would be 5 x 2, which equals 10. Then, don’t forget to add the number you carried to the product of the multiplication, in this case, adding 2 to the 10, which gives you 12. Then, simply write 12 in front of the 5 of your answer, for a complete answer of 125.

Here’s what the multiplication looks like:

Steps 1 and 2

Step 3

Let’s try this one more time. Here’s the example:

Following the steps above, it would look like this:

- Multiply 6 x 4 which equals 24.
- Split up 24. Write the 4 in the ones column of the answer. Carry the 2 above the tens digit of the top number. (This is in red in the diagram below.)
- Multiply the 4 times the 3, then add the 2 you had carried. You would get 4 x 3 = 12, then 12 + 2 = 14. Write the 14 in front of the 4, for a complete answer of 144.

Here’s the problem worked out:

## Multiplying Two Digit Numbers by Two Digit Numbers

After you get used to multiplying 2 digit numbers by 1 digit numbers, you’ll move on to multiplying 2 digit numbers by 2 digit numbers. There are a few added steps to this process, so pay close attention to the examples.

First, this is what the problem will look like:

You will follow the first few steps as if you were multiplying a 2 digit number by a 1 digit number. Start by multiplying the ones digit on bottom by the ones digit on top (in this example, 5 x 3). Remember to split the number—the ones digit goes in your answer, the tens digit gets carried above the tens column in your multiplication problem.

Now continue with multiplication by multiplying the ones digit of the bottom number (5) by the tens digit of the top number (4) and then adding the carried number (1). In this problem, you would do 5 x 4 = 20, 20 + 1 = 21. Write the 21 in front of the 4. Your answer this far should read 214, and the columns should be aligned (ones, tens, hundreds). Here’s what your problem looks like so far:

Now, the next step is very important, so watch closely. Before you move on, you need to put a zero (0) in the ones column of your answer, beneath your ones digit from the first set of multiplication. In the diagram, this is done in red:

Now, you continue with multiplication. For the next round of multiplication, you are going to be using the tens digit of the bottom number (2). First, you will multiply the tens digit of the bottom number by the ones digit of the top number. In the diagram, these numbers will be circled in red, to help you follow along. You will then split the number, like you did in the first part. The ones digit will be written in front of the 0, and the tens digit (if there is one) will be carried. In this problem, when you multiply 2 x 3, you get 6, which does not have a tens digit, so you will have nothing to carry. In the diagram, the 6 is also written in red, and is placed in front of the 0. Here’s what these steps look like:

Last, you’ll be multiplying the tens digit of the bottom number (2) by the tens digit of the top number (4). This will be circled in red on the diagram, to help you follow along. The product of this multiplication is written in front of the 6, in the same row, like this:

Now, you have two rows of answers; one says 215, and the next one says 860. You are going to add those numbers together in order to get your final answer. You don’t even have to re-write them; just draw an answer bar beneath the bottom row, and put an addition sign in front of the 860. It is very important here to make sure that your columns are lined up! If you have numbers squished together, or too far apart, you won’t be able to add the numbers together. Here’s what the last step looks like:

Thus, your final answer is 1075. Congrats, you made it through!

Want one more example? Here’s the problem—see if you can work it out yourself. The solution will be shown, all at once, in the second diagram.

Ready for the answer? Here’s the solution, worked out. The two numbers you should have carried are in red. The zero that you add in to the second row of your products is also in red, like last time.

## Multiplying Three Digit Numbers by Two Digit Numbers

More advanced multiplication problems will ask you to multiply three digit numbers by two digit numbers. Don’t worry, it’s really similar to the two digit by two digit multiplication, you are just working with a few more numbers. We’ll go through it step by step, so that you can do the same when you see a problem like this. Here’s our example:

First, we’ll multiply by the ones digit of the bottom number, which is 6 in this problem. We’ll multiply the 6 by the ones digit of the top number (2), then by the tens digit of the top number (1), then by the hundreds digit of the top number (3). We’ll carry if we need to, the carried numbers will be in red in our diagram. Remember that if you carry a number, it is added in to the next multiplication you do.

Here’s what the multiplication looks like for the ones digit of our bottom number:

Now—remember! The really important step! In the next row, we have to put a zero (0) in the ones column! Otherwise, our problem won’t line up right, and we’ll get an incorrect answer. Here’s the step showing you where to add the zero:

Next, you’re going to take the tens digit of the bottom number and multiply it by all three digits in the top number—first you’ll multiply it by the ones digit (2), then the tens digit (1), then the hundreds digit (3). Remember, if you get an answer that is 10 or bigger, you have to split the number and carry the tens digit. Also, make sure you’re lining up your columns so that your addition comes out correctly later on.

Here’s what the next part looks like, split up into steps. First, we multiply the tens digit of the bottom number by the ones digit of the top number, like this (multiplied numbers are circled so you can follow along):

Notice that in this step, we had to split up 10—we wrote the 0 in the answer column, but we carried the 1 onto the next number we’ll be multiplying, which is the 1.

Now, for the next step: multiplying the tens digit of the bottom number by the tens digit of the top number (again, the numbers are circled in red to help you follow along):

Notice that in this step, I multiplied 5 x 1 = 5, and then added 1 (because we had carried it) so I wrote 6 in the answer column.

Our last step is to multiply the tens digit of the bottom number (5) by the hundreds digit of the top number (3). Once again, these numbers are circled in red to help you follow along. The product is written in front of the 6; remember that it’s very important to keep these columns lined up for our addition problem that we’ll complete in just a few minutes.

Now, we have to put our addition sign in front of the bottom row of our products, and add those two rows together. Here’s that step:

So, your final answer is 17,472.