Multi-Digit Addition and Subtraction

Adding and subtracting large numbers is the same skill you used with smaller numbers, just stacked into more columns. Line up the digits by place value, work from right to left, and regroup whenever a column needs more or less than its place can hold.

Lining Up the Columns

• Stack the numbers so ones sit under ones, tens under tens, hundreds under hundreds, and so on.
• Keep commas and place-value columns aligned so digits do not drift sideways.
• If one number is shorter, imagine zeros on its left so every column has a digit.

Adding with Regrouping (Carrying)

• Add the digits in the ones column first.
• If the column sum is 10 or more, write the ones digit and carry the tens digit to the next column.
• Repeat for tens, hundreds, thousands, and beyond — including any carried 1.
• Example: 4,827 + 3,596 = 8,423 (carries from ones, tens, and hundreds).

Subtracting with Borrowing

• Subtract the digits in the ones column first.
• If the top digit is smaller than the bottom digit, borrow 1 from the next column on the left.
• The borrowed 1 becomes 10 in the current column, and the column you borrowed from drops by 1.
• Example: 6,204 - 1,847 = 4,357 (borrow chains from the hundreds through the zero in the tens).

Borrowing Across Zeros

• When the next column on the left is 0, you cannot borrow from it directly.
• Keep moving left until you reach a digit greater than 0, borrow 1 from there, and pass 9s back through every zero you skipped.
• In 6,204 - 1,847 the tens column is 0, so the borrow comes from the hundreds: 2 becomes 1, the 0 in tens becomes 10, then drops to 9 after lending 1 to the ones.

Estimating to Check

• Round each number to the nearest hundred or thousand before computing.
• Add or subtract the rounded numbers to get a quick estimate.
• Compare the estimate to your exact answer — if they are far apart, recheck your work.
• Example: 4,827 + 3,596 is about 5,000 + 4,000 = 9,000, so 8,423 is reasonable.