Multi-digit addition and subtraction

Step 6 · Long division and equivalent fractions topics

Add and subtract numbers with many digits by lining up the places, regroup across zeros, and check answers with an estimate.

Adding in columns

Write the numbers one under the other with the ones lined up. Add each column from the right, and carry 1 to the next column whenever a column makes 10 or more.

Example: Adding in columns

What is 4,586 + 2,739?

Ones: 6 + 9 = 15. Write 5, carry 1.
Tens: 8 + 3 + 1 = 12. Write 2, carry 1.
Hundreds: 5 + 7 + 1 = 13. Write 3, carry 1.
Thousands: 4 + 2 + 1 = 7.

Answer7,325

Row	Thousands	Hundreds	Tens	Ones
First	4	5	8	6
Second	2	7	3	9
Sum	7	3	2	5

Subtracting in columns

Subtract each column from the right. When the top digit is smaller, regroup: take 1 from the next column to the left, which gives this column 10 more.

Example: Regrouping across zeros

What is 6,003 − 2,457?

Ones: 3 − 7 needs regrouping, but the tens and hundreds are 0.
Take 1 thousand: 6,003 becomes 5 thousands, 9 hundreds, 9 tens and 13 ones.
13 − 7 = 6, 9 − 5 = 4, 9 − 4 = 5, 5 − 2 = 3.

Answer3,546

Another way: take 1 from both numbers first. 6,002 − 2,456 needs no regrouping and gives the same 3,546.

Checking with estimates

Round each number before you work and find a rough answer. If the exact answer is far from it, look for a slip.

Example: Checking a sum

Rosa adds 38,914 + 21,375 and gets 50,289. Is that right?

Round to thousands: 39,000 + 21,000 = 60,000.
50,289 is about 10,000 too small.
Redo it: 38,914 + 21,375 = 60,289.

AnswerNo. It is 60,289.

You can also check a subtraction by adding: 3,546 + 2,457 = 6,003, so 6,003 − 2,457 = 3,546 is right.

Try it yourself

Work each one on paper first, then open the answer to check.

What is 3,658 + 4,275?
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7,933.
What is 9,000 − 3,742?
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5,258.
What is 52,306 + 17,895?
Show answer
70,201.
What is 80,415 − 26,738?
Show answer
53,677.
Estimate 61,920 − 29,875 by rounding to the nearest thousand.
Show answer
62,000 − 30,000 = 32,000.