Multiplication and Division: Introduction to Multiplication

Lesson 1: Introduction to Multiplication

What is multiplication?

When you multiply, you're basically adding a certain number more than once. For instance, if you eat 4 pieces of candy, then you eat another 4, then 4 more, you can say that you multiplied the amount of candy you ate.

3 sets of 4 pieces of candy

Multiplication happens all the time in real life. For example, consider the situation below.

  • Imagine that you buy a 6-pack of soda. You have 1 set of 6 cans.

  • In multiplication terms, we'd say that you have 1 x 6 cans. You can read that as one times six.

  • What if you buy 2 6-packs?

  • Now you have 2 sets of 6 cans, or 2 x 6 cans. That's 2 times as many cans as you had before!

  • This can go on forever. What about 3 x 6 cans, or 3 times as many cans?

  • Now you have 8 x 6 cans. This is 8 times as many cans as you had at the beginning.

  • It's important to know that the numbers in a multiplication expression can be written in any order.

  • So, 8 x 6 could also be written as 6 x 8.

  • In other words, 6 x 8 = 8 x 6.

  • So if you bought 6 sets of 8 cans each...

  • So if you bought 6 sets of 8 cans each... it would be the same as having 8 sets of 6 cans each. You'd have the exact same number of cans.

Writing multiplication expressions

As you just saw, a multiplication expression is written like this:

2 x 6

You can read that expression as two times six. The multiplication symbol (x) can also be called the times symbol. Remember, you always put it between the numbers you want to multiply.

Many real-life situations can be expressed with multiplication. For instance, imagine that you want to make three cakes. The recipe says that each cake will need two eggs. In other words, you need 3 x 2 eggs.

3 x 2

Try this!

Write the following situations as multiplication expressions. Don't try to solve them yet.

You have six pairs of two socks each.

You need to take two pills four times a day.

Each bag contains nine donuts. You buy three bags.

Solving multiplication problems

You can use counting and adding to solve some small, simple multiplication problems. For example, on the last page, we were trying to figure out how many eggs we'd need to make three cakes. Each cake needed two eggs, so we wrote the problem like this:

3 x 2

As you know by now, that expression means three times two, or 3 cakes with 2 eggs each. It's a simple problem. To solve it, you can either count the eggs or add them: 2 + 2 + 2. Either way, the answer is 6. We know that 3 x 2 = 6.

3 x 2 = 6

While this works for small problems, counting large numbers can take a long time— and it's pretty boring too. For this reason, most people memorize common multiplication problems so that they can solve them quickly. If this sounds hard, don't worry. The more you practice, the easier it will be to remember the answers to problems.

Until then, you can solve multiplication problems by using a multiplication table. It's also called a times table. A times table is a chart with the answers to all of the multiplication problems that use the numbers 1 through 12. It's simple to use. Click through the slideshow below to learn how.

  • This is a times table.

  • At the top of the times table, you can find the numbers 1 through 12. They're in order from left to right.

  • Each of the numbers on top is at the start of a column. For example, this is the column that goes with 5. All of the numbers in this column are multiples of 5. This means that they're all numbers you can get by multiplying 5.

  • You can also find the numbers 1 through 12 on the left side of the times table. Here, the numbers are in order from top to bottom.

  • Each of these numbers is the start of a row. This row contains the multiples of 4.

  • Let's try solving a problem with the times table. We'll start with 7 x 3.

  • In 7 x 3, find the first number we're multiplying by on the left of the times sign. That's 7.

  • Find the 7 at the top of the chart.

  • Next, look at the second number we're multiplying by on the right of the times sign. In 7 x 3, that's 3.

  • Find the 3 on the side of the chart.

  • The answer will be in the square where the 7's column and the 3's row meet and overlap.

  • It's this square, 21. So 7 x 3 is 21.

  • Let's try that again. This time, we'll solve 5 x 9.

  • First, for 5 x 9, we find the 5's column.

  • Next, for 5 x 9, we'll find the 9's row.

  • Finally, we find the square where the column and the row meet. It's 45. So 5 x 9 = 45.

You might have noticed there is no 0 row in the times table. That's because zero times anything is just zero. For example, 5 x 0 = 0 and 0 x 100 = 0.

Try this!

Solve the following multiplication problems. You can use the times table as a reference if needed. Check your answer by typing it into the box.

4 x 6 =
7 x 11=
5 x 1 =


Practice multiplication with these problems. If you want, you can use the times table. There are 3 sets of problems. Each set has 5 problems.

Set 1

3 x 2 =
4 x 1 =
2 x 5 =
4 x 3 =
2 x 7 =

Set 2

7 x 6 =
4 x 6 =
8 x 7 =
9 x 10 =
12 x 5 =

Set 3

4 x 9 =
8 x 1 =
6 x 5 =
10 x 8 =
12 x 12 =