Adding Three-Digit Numbers
Grade 4 students master adding three-digit numbers with carrying in Saxon Math Intermediate 4 Chapter 2. The process follows place value columns from right to left: ones first, then tens, then hundreds. For 358 + 274: ones 8+4=12 (write 2, carry 1); tens 1+5+7=13 (write 3, carry 1); hundreds 1+3+2=6. Answer: 632. Students learn carrying is like trading ten one-dollar bills for a ten-dollar bill—the total remains the same, organized differently. The consistent warning: always look for and include any carried digit before summing a column.
Key Concepts
Property To add large numbers, stack them vertically. Add the ones column first, then tens, then hundreds. If a column's sum hits 10 or more, you regroup by carrying the extra digit to the next column on the left. This is just like trading ten 1 dollar bills for one 10 dollar bill.
Examples Example 1: Add 579 dollars and 186 dollars by aligning them vertically and regrouping.
$$ \begin{array}{r} \overset{1}{5}\overset{1}{7}9 \\ + 186 \\ \hline 765 \\ \end{array} $$.
Common Questions
What is the step-by-step process for adding two three-digit numbers?
Step 1: Write numbers vertically, aligned by place value. Step 2: Add the ones column; if 10 or more, write the ones digit and carry the tens digit. Step 3: Add the tens column plus any carried digit; repeat the carry rule. Step 4: Add the hundreds column plus any carried digit.
How do you add 358 + 274?
Ones: 8+4=12. Write 2, carry 1. Tens: 1+5+7=13. Write 3, carry 1. Hundreds: 1+3+2=6. Answer: 632.
What happens when both the ones and tens columns produce carries?
Apply the carry rule at each step independently. A carry from the ones goes to the tens; a carry from the tens goes to the hundreds. Each carry is a separate 1 that must be added to the next column.
Why must you add the carried digit before summing the column's original digits?
Adding the carry first prevents accidentally overlooking it. The carry from the previous column is equally important as the printed digits—missing it always produces an answer that is 10 too small.
How do you add 675 + 175?
Ones: 5+5=10. Write 0, carry 1. Tens: 1+7+7=15. Write 5, carry 1. Hundreds: 1+6+1=8. Answer: 850.
What real-world problem requires adding three-digit numbers?
Combining page counts of two books, totaling two separate cash register receipts, adding up scores from two rounds of a game, or finding the total weight of two packages all require three-digit addition with carrying.