Adding Three Digit Numbers Without Regrouping
Adding three-digit numbers is really just working three simple addition problems that are connected together. Follow these steps to work a three-digit addition problem without regrouping:
1. Line up your problem, so the ones places of each number are together. Make sure the tens places and hundreds places are also lined up.
2. Start with the ones place. Add the two numbers together. In the example above, you would add together 5 + 2 = 7. The ones place answer is 7.
3. Now add together the tens place. The two numerals in the tens place in the example are 2 + 3 = 5. The tens place answer is 5 (which stands for 50).
4. Finally, add together the hundreds place. The numerals in the hundreds place are 1 + 4 = 5 (which stands for 500). So, the answer to the above example of adding three-digit numbers is 557.
Adding Three Digit Numbers with Regrouping
Regrouping is when you add together two numbers in a three-digit addition problem, and your sum is a two-digit answer. You have to "regroup" or "carry" to solve the problem. For example:
You follow the same steps as you did for the problem above when you were adding three-digit numbers. The only difference is you will have to regroup. First, you add the ones place, which is 5 + 7, and you get 12. You write down the 2 in the ones place, and you have to regroup the 1 (which actually stands for 10) to be with the other tens. When you regroup, you write the number you carried above the other numbers in the tens place. (See the completed problem below for an example). The other tens in this problem are 3 + 9. So, now you are working:
1 + 3 + 9=13 (which is actually 130). You have to regroup again. You write down the 3 as the answer for the tens place, and you carry the 1 to the hundreds place. The next problem you have to work is for the hundreds place. You add 1 + 4 + 2 = 7. So, your answer is 732. The problem looks like this when you are finished.
Subtract Three-Digit Numbers
When you subtract three-digit numbers, you have to make sure that the number with the greatest value is on top. The number with the least value is written underneath this number. Just like with addition problems, you have to make sure the digits are lined up correctly, so the ones places, tens places, and hundreds places match. Adding and subtracting three-digit number problems are easier if you take your time and follow the steps.
1. Start with the ones place. You subtract 7 -5 =2. Write down the 2. It is important to remember that you always take the top number first and then subtract the bottom number, as we are doing in each of these examples.
2. Go to the tens place and subtract those digits. 8 – 4 = 4. Write down the 4 (which stands for 40).
3. Now subtract the hundreds place, which in the above example is 9 – 3 = 6 (which stands for 600).
4. The answer to this problem is 642. Remember, to always start with the ones place when you are adding and subtracting three-digit numbers.
Subtract Three-Digit Numbers with Regrouping
Regrouping can occur when you are adding and subtracting three-digit numbers. It looks different in subtraction problems than it does in addition problems, but it is the same idea. Look at this example problem:
1. The number with the greatest value is on the top, which is correct for a three-digit subtraction problem. However, the ones place gives you this problem to work: 5 – 7 = You do not want to work a problem like this, and so you must regroup to work this problem. You are going to "borrow" 1 ten from the tens place. That will make the 5 in this subtraction problem 15 (5 + 10 = 15). Now, you are going to work 15 – 7 = 8.Write down the 8 in the ones place for the answer.
2. Now, when you go to the tens place to subtract it, remember, you have borrowed 1 ten from the 4 tens, so you have to change it to a 3. (4 tens – 1 ten = 3 tens). So, now the problem you are working is 3 – 2 = 1 (which stands for 10). Write down the 1 in the tens place for the answer.
3. Finally, you will subtract the hundreds place, just like always, to finish the problem. 7 – 3 = 4 (which stands for 400).
4. The answer to the example problem is 418.
The important thing to remember when you are subtracting any three-digit numbers is to start at the ones place and always borrow from the next place to the left, unless it is a zero. Then you have to borrow from the next place to the left that is not a zero. Take your time with subtraction and go step by step!
Online Resources and Examples
For more information on adding and subtracting three-digit numbers, you might want to check out: Cool Math 4 Kids 3-Digit Addition or Cool Math 4 Kids 3-Digit Subtraction (see references for further information).
With practice, you'll be adding and subtracting three-digit numbers correctly in no time.
- 3 Digit Subtraction – http://www.coolmath4kids.com/subtraction/07-subtraction-lesson-three-digit-numbers-01.html
- 3 Digit Addition – http://www.coolmath4kids.com/addition/06-addition-lesson-three-digit-numbers-01.html