Adding Three-Digit Numbers
Grade 4 students learn to add three-digit numbers with regrouping in Saxon Math Intermediate 4 Chapter 2. Regrouping means exchanging 10 ones for 1 ten or 10 tens for 1 hundred when a column sum reaches 10 or more. For 357 + 286: ones 7 + 6 = 13 (write 3, carry 1); tens 1 + 5 + 8 = 14 (write 4, carry 1); hundreds 1 + 3 + 2 = 6. Sum: 643. The most frequent error is forgetting to add the carried digit to the next column—it must always be included.
Key Concepts
New Concept We can exchange 10 ones for 1 ten and 10 tens for 1 hundred. This process is called regrouping.
What’s next Next, you’ll apply this regrouping method to add money and solve word problems, solidifying your understanding of place value.
Common Questions
How do you add three-digit numbers with regrouping?
Write numbers vertically aligned by place value. Add the ones column; if the sum is 10 or more, write the ones digit and carry the tens digit. Repeat for the tens and hundreds columns, always adding any carried digit.
How do you solve 357 + 286?
Ones: 7 + 6 = 13. Write 3, carry 1. Tens: 1 (carry) + 5 + 8 = 14. Write 4, carry 1. Hundreds: 1 (carry) + 3 + 2 = 6. Answer: 643.
When is regrouping required in addition?
Regrouping is required whenever the sum of digits in any column equals 10 or more. You cannot write two digits in one place-value slot, so you write the ones digit of the sum and carry the tens digit to the next column.
What is the analogy between regrouping in addition and trading money?
Collecting 10 one-dollar bills and trading them for a single ten-dollar bill is identical to carrying in addition: you exchange 10 ones for 1 ten, keeping the total value the same while organizing the digits.
What is the most critical mistake to avoid when adding with regrouping?
Forgetting to add the carried digit to the next column. After carrying a 1 to the tens column, that 1 must be added to the tens digits before you record the tens answer. Skipping it gives a wrong answer.
Can you need to regroup more than once in a single addition problem?
Yes. If both the ones column and the tens column produce sums of 10 or more, you regroup twice—once from ones to tens, and once from tens to hundreds. Each column's carry must be included in the next column.