Addition and Subtraction

Subtracting Two- and Three-Digit Numbers

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In Introduction to Subtraction, we learned that **counting** and using **visuals** can be useful for solving basic subtraction problems. For instance, say you have **9** apples and you use **6** to make a pie. To find out how many apples are left, you could represent the situation like this:

It's easy to count and see that **3** apples are left.

What if you need to solve a subtraction problem that starts with a large number? For instance, let's say instead of making an apple pie, you want to pick apples from an apple tree. The tree has **30** apples and you pick **21**. We could write this as **30 - 21**.

You might see why counting to solve this problem isn't a good idea. When you have a subtraction problem that starts with a large number, it could take a long time to set up the problem. Imagine the time it would take to count out 30 objects and then take away 21! Also, it would be easy to lose track as you counted. You could end up with the wrong answer.

For this reason, when people solve a subtraction problem with large numbers, they set up the problem in a way that makes it easy to solve one step at a time. Let's see how this works with another problem: **79 - 13**.

We can see that **79 - 13 **and mean the same thing — they're just written differently.

If you feel comfortable with the subtraction skills from Introduction to Subtraction, you're ready to start solving stacked subtraction problems.

In the slideshow, you saw that stacked subtraction problems are always solved from **right to left**. The expressions below are solved the same way. First, the** bottom right** digit is subtracted from the **top** right digit. Then, the bottom **left** digit is subtracted from the **top** left digit.

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

56 - 40 =

29 - 19 =

75 - 23 =

Stacked subtraction can also be used for finding the difference of larger numbers. No matter how many digits there are, you subtract the same way every time — from right to left.

These subtraction problems have larger numbers. Solve them, and then check your answer by typing it into the box.

225 - 100 =

199 - 21 =

634 - 623 =

Sometimes when you subtract, you will notice that the top digit is smaller than the bottom. For example, take a look at this problem:

Normally, we'd start on the right with 5 - 9. However, since 9 is bigger than 5, we can't subtract normally. Instead, we have to use a technique called **borrowing**.

Let's see how it works.

As you borrow, always cross out the digit you borrow from and write the new value **above **it. Remember to always place the 1 **next **to the smaller digit.

Try these problems to practice borrowing. Check your answer by typing it into the box.

73 - 14 =

46 - 8 =

151 - 26 =

Sometimes the top number might have two or more digits that are smaller than the digits beneath them. In that case, you'll need to borrow more than once. It will always work the same way. You'll always **subtract 1** from the digit to the left and place 1** next** to the smaller digit.

In some cases, you might notice that the number to the left is zero. Check out the slideshow below to see an example of what to do.

Try solving these subtraction problems to practice borrowing more than one time. Check your answer by typing it in the box.

200 - 94 =

654 - 598 =

101 - 43 =

In the last few lessons, you learned how to solve addition and subtraction problems. As you practice these math skills, it's a good idea to get into the habit of** checking your work**. Checking will help you know if your answers are correct. When you're ready to check the answer to subtraction problems, you'll need to use addition.

Practice subtracting these problems. You'll have to use borrowing to solve some of the problems. There are **4** sets of problems with **3** problems each.

45 - 34 =

22 - 10 =

98 - 63 =

15 - 9 =

92 - 68 =

83 - 57 =

50 - 25 =

62 - 12 =

98 - 37 =

220 - 119 =

115 - 43 =

609 - 210 =

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