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Addition and Subtraction

Adding Two- and Three-Digit Numbers

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Using Carrying

On the last page, you practiced adding vertically stacked numbers. Some problems need an extra step. For example, can you add the numbers in this expression?

When you tried to add the digits on the right— 5 and 9— you might have noticed that there was no room to write the sum, 14. When the sum of two digits in a math problem is greater than 9, the normal way of adding stacked numbers won't work. You'll have to use a technique called carrying.

• Let's see how it works. We'll try this problem, 25 + 39.

• As usual, we'll start by adding the digits on the right. Here, that's 5 and 9.

• 5 + 9 is 14, but there's no room to write both digits in 14 underneath the 5 and 9.

• We'll write the right digit, 4, under the line...

• We'll write the right digit, 4, under the line... then we'll carry the left digit, 1, up to the next set of digits in the problem.

• Do you see what we did? Our sum was 14. We put the 4 underneath the line, and carried the 1 and placed it above the next set of digits.

• Next, we'll add the left digits. Since we carried the 1, we'll add it too.

• 1 + 2 + 3 is 6, so we'll write 6 below the line.

• We're done. 25 + 39 = 64.

• Let's practice with one more problem: 178 + 42.

• As always, start by adding the digits on the right. Here, that's 8 + 2.

• 8 + 2 is 10, so it looks like we'll have to carry.

• The 0 stays underneath the 8 and the 2.

• Carry the 1 and place it above the next set of digits to the left.

• Now move left to add the next set of digits. Since we carried the 1, add it too.

• 1 + 7 + 4 = 12.

• Put the right number, 2, under the digits we added.

• Carry the 1 and place it above the next column to the left.

• To finish, add this column. Remember to include the 1 we just carried.

• 1 + 1 + nothing is 2, so we'll write 2 underneath the 1.

• We're done. Our answer is 220. 178 + 42 = 220.

As you carry, be careful to keep track of the various numbers. If you're writing problems down, be sure to write the carried digits in small print above the column of digits to the left.

Now you try it. Solve these problems by carrying.