Adding and Subtracting Whole Numbers

Addition and subtraction are the two most fundamental operations in mathematics. Everything else — multiplication, division, fractions, algebra — builds on them. This page covers multi-digit addition with carrying and subtraction with borrowing, two skills that trip up many learners but follow simple, predictable rules.

Addition: The Basics

Addition combines two or more numbers into a single sum. Line up the digits by place value and add column by column, starting from the ones place (rightmost column).

Example 1: Add 342 + 215

$\begin{array}{r} 342 \\ +\; 215 \\ \hline 557 \end{array}$

• Ones: $2 + 5 = 7$
• Tens: $4 + 1 = 5$
• Hundreds: $3 + 2 = 5$

Answer: $557$

Addition with Carrying (Regrouping)

When a column adds up to 10 or more, write the ones digit and carry the tens digit to the next column.

Example 2: Add 478 + 356

$\begin{array}{r} ^1\;^1 \\ 478 \\ +\; 356 \\ \hline 834 \end{array}$

• Ones: $8 + 6 = 14$ → write 4, carry 1
• Tens: $7 + 5 + 1 = 13$ → write 3, carry 1
• Hundreds: $4 + 3 + 1 = 8$

Answer: $834$

Example 3: Add 1,897 + 3,654

• Ones: $7 + 4 = 11$ → write 1, carry 1
• Tens: $9 + 5 + 1 = 15$ → write 5, carry 1
• Hundreds: $8 + 6 + 1 = 15$ → write 5, carry 1
• Thousands: $1 + 3 + 1 = 5$

Answer: $5{,}551$

Subtraction: The Basics

Subtraction finds the difference between two numbers. Line up digits by place value and subtract column by column, starting from the ones place. The larger number goes on top.

Example 4: Subtract 785 - 342

$\begin{array}{r} 785 \\ -\; 342 \\ \hline 443 \end{array}$

• Ones: $5 - 2 = 3$
• Tens: $8 - 4 = 4$
• Hundreds: $7 - 3 = 4$

Answer: $443$

Subtraction with Borrowing (Regrouping)

When a digit on top is smaller than the digit below it, you must borrow from the next column to the left. Take 1 from that column (reducing it by 1) and add 10 to the current column.

Example 5: Subtract 532 - 178

Start from the right:

• Ones: $2 - 8$? Cannot do — borrow from tens. Tens goes from 3 to 2, ones becomes 12. Now $12 - 8 = 4$
• Tens: $2 - 7$? Cannot do — borrow from hundreds. Hundreds goes from 5 to 4, tens becomes 12. Now $12 - 7 = 5$
• Hundreds: $4 - 1 = 3$

Answer: $354$

Check: $354 + 178 = 532$ ✓

Example 6: Subtract 4,003 - 1,847

This one requires borrowing across zeros, which is the trickiest case:

• Ones: $3 - 7$? Borrow from tens — but tens is 0. Borrow from hundreds — also 0. Go to thousands: reduce 4 to 3, making hundreds 10. Then borrow from hundreds: reduce 10 to 9, making tens 10. Then borrow from tens: reduce 10 to 9, making ones 13.
• Ones: $13 - 7 = 6$
• Tens: $9 - 4 = 5$
• Hundreds: $9 - 8 = 1$
• Thousands: $3 - 1 = 2$

Answer: $2{,}156$

Check: $2{,}156 + 1{,}847 = 4{,}003$ ✓

Checking Your Work

The best way to verify subtraction is by adding back: if $a - b = c$, then $c + b$ should equal $a$.

The best way to verify addition is by subtracting: if $a + b = c$, then $c - b$ should equal $a$.

Adding and Subtracting Multiple Numbers

When adding more than two numbers, you can add them in any order (the commutative and associative properties of addition). Group numbers that are easy to add mentally:

Example 7: Add $28 + 45 + 72 + 55$

Group: $(28 + 72) + (45 + 55) = 100 + 100 = 200$

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Line up place values when adding or subtracting vertically
• Carrying: when a column totals 10+, write the ones digit and carry the tens
• Borrowing: when the top digit is too small, borrow 10 from the next column to the left
• Borrowing across zeros: chain the borrowing until you reach a nonzero digit
• Check your work: use the inverse operation (add to check subtraction, subtract to check addition)

Return to Arithmetic for more foundational math topics.