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H.4 Add two numbers up to five digits

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Understanding addition with larger numbers

Addition is the mathematical process of combining two or more numbers to find their total. When adding larger numbers, we use a method called regrouping (sometimes called "carrying") to help us add correctly.

Key terms:
  • Addends: The numbers being added together
  • Sum: The answer to an addition problem
  • Place Value: The value of a digit based on its position in a number
  • Regrouping: Moving a group of ten from one place value to the next higher place value
Remember

Always line up numbers by their place values before adding. The ones digits should be in a straight column, the tens digits in another column, and so on.

Adding without regrouping

When the digits in each place value column add up to 9 or less, we can simply add each column from right to left without regrouping.

Example:
4,321
+ 1,234
5,555

Step-by-step explanation:

  • Start with the ones place: 1 + 4 = 5
  • Move to the tens place: 2 + 3 = 5
  • Next, the hundreds place: 3 + 2 = 5
  • Finally, the thousands place: 4 + 1 = 5
Tip

When no regrouping is needed, each column's sum will be 9 or less. Always double-check your work by adding in the opposite direction!

Adding with regrouping in one place value

When the digits in one column add up to 10 or more, we need to regroup. We write the ones digit of the sum in that column and "carry" the tens digit to the next column on the left.

Example:
3,467
+ 1,785
5,252

Step-by-step explanation:

  • Ones place: 7 + 5 = 12. Write 2 in ones place, carry 1 to tens place.
  • Tens place: 6 + 8 + 1 (carried) = 15. Write 5 in tens place, carry 1 to hundreds place.
  • Hundreds place: 4 + 7 + 1 (carried) = 12. Write 2 in hundreds place, carry 1 to thousands place.
  • Thousands place: 3 + 1 + 1 (carried) = 5. Write 5 in thousands place.
Remember

When regrouping, always add the carried number to the next column. The carried number is always 1 because we're working in base ten.

Adding with multiple regrouping

Sometimes we need to regroup in multiple place value columns. The process is the same, but we repeat it for each column where the sum is 10 or more.

Example:
4,789
+ 3,567
8,356

Step-by-step explanation:

  • Ones place: 9 + 7 = 16. Write 6 in ones place, carry 1 to tens place.
  • Tens place: 8 + 6 + 1 (carried) = 15. Write 5 in tens place, carry 1 to hundreds place.
  • Hundreds place: 7 + 5 + 1 (carried) = 13. Write 3 in hundreds place, carry 1 to thousands place.
  • Thousands place: 4 + 3 + 1 (carried) = 8. Write 8 in thousands place.
Tip

When you have multiple regroupings, work slowly and carefully. It might help to write the carried numbers lightly above the columns as you work.

Adding five digit numbers

When adding five-digit numbers, we follow the same process but extend it to the ten-thousands place. Always start from the ones place and move left.

Example:
45,678
+ 23,456
69,134

Step-by-step explanation:

  • Ones place: 8 + 6 = 14. Write 4 in ones place, carry 1 to tens place.
  • Tens place: 7 + 5 + 1 (carried) = 13. Write 3 in tens place, carry 1 to hundreds place.
  • Hundreds place: 6 + 4 + 1 (carried) = 11. Write 1 in hundreds place, carry 1 to thousands place.
  • Thousands place: 5 + 3 + 1 (carried) = 9. Write 9 in thousands place.
  • Ten-thousands place: 4 + 2 = 6. Write 6 in ten-thousands place.
Remember

For five-digit numbers, the leftmost digit is in the ten-thousands place. Make sure to include commas when writing numbers with four or more digits.

Checking your work

It's important to check your addition to make sure you've calculated correctly. One effective method is to add the numbers in the opposite direction.

Checking Method:

If you added: 2,345 + 1,678 = 4,023

Check by adding: 1,678 + 2,345

1,678
+ 2,345
4,023

Since we get the same answer, our original calculation was correct!

Tip

Another way to check your work is to estimate first. Round each number to the nearest thousand or hundred, add them, and see if your actual answer is close to your estimate.

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