Multiplication and Division

Multiplying 2- and 3-Digit Numbers

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When you multiply a number or amount, you're **increasing** it many times. In Introduction to Multiplication, you learned that multiplication can be a way to understand things that happen in real life. For instance, imagine that a store sells boxes of pears. The small boxes contain **five** pears each. You buy **two**. You could write the situation like this, and use the **times table** to solve it:

Now, imagine that you decide to buy **two** larger boxes containing **14** pears each. That situation would look like this:

This problem is harder to solve. Counting the pears would take a while. Plus, there's no 14 on the times table. Fortunately, there's a way to write the problem so that you can break it into smaller pieces. It's called **stacking**. It means that we'll write the numbers **on top of one another** instead of side by side.

At first glance, stacked multiplication problems might look pretty complicated. Don't worry! If you can solve the problems in Introduction to Multiplication, you can learn to solve these problems too. To multiply large numbers, you'll use the same basic skills you use to multiply small ones. You can even use the same tools, like** times tables**.

Let's see how solving stacked multiplication problems works.

Stack and solve these multiplication problems. Then, check your answer by typing it into the box.

31 x 3 =

24 x 2 =

40 x 8 =

On the last page, you practiced multiplying vertically stacked numbers. Some problems need an extra step. Let's look at the following problem:

If you try to multiply 9 x 5, you might notice that there is no room to write the product, 45. When the product of two numbers is** greater than 9**, you'll need to use a technique called **carrying**. If you know how to add large numbers, you might remember using carrying in addition too. Let's see how it works in multiplication.

Stack and solve these multiplication problems. Then, check your answer by typing it into the box.

25 x 9 =

98 x 2 =

103 x 5 =

On the past few pages, you've practiced multiplying large numbers with small ones. What happens when you have to multiply two large numbers?

For example, imagine that your cell phone bill is **$43 a month**. There are **12** months in a year, so to find out how much you pay for your phone every year, you could solve for 43 x 12. You'd write the expression like this:

This problem might look hard at first, but don't worry. If you can multiply small numbers, you can multiply large ones too. All you have to do is divide this large problem into a few smaller ones. As always, you can use your **times table** to help.

Stack and multiply these two-digit numbers. Then, check your answer by typing it in the box.

33 x 21 =

52 x 17 =

81 x 34 =

Multiplying large numbers always works the same way, no matter how many digits the numbers have. When you're multiplying, be careful about writing the numbers in the correct places. Let's look at a problem with two **3-digit** numbers to see how this works with even larger numbers.

What a huge number! If that problem seemed complicated, don't worry. You'll rarely need to multiply such large numbers. When you do, you can always use a calculator. Still, it's good to know how. If you can multiply these problems, you can multiply anything.

Practice multiplying large numbers. Then check your answer by typing it in the box.

13 x 3 =

42 x 4 =

21 x 9 =

63 x 2 =

52 x 3 =

76 x 5 =

24 x 8 =

63 x 7 =

18 x 6 =

35 x 9 =

21 x 18 =

33 x 34 =

46 x 29 =

17 x 12 =

55 x 48 =

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