Add & subtract four-digit numbers
Theory
Adding and subtracting four-digit numbers is a Year 4 maths skill: line up the thousands, hundreds, tens and ones, work from the ones column, regroup when a column reaches ten, and trade when a top digit is too small to subtract from. This page also shows how to estimate, check with the inverse operation, and find missing numbers and digits. Curriculum: VC2M4N06 / AC9M4N06.
A four-digit number has thousands, hundreds, tens and ones. In \(4735\) there are \(4\) thousands, \(7\) hundreds, \(3\) tens and \(5\) ones. To add or subtract, line the numbers up so each place sits under the same place, then work one column at a time, starting with the ones.
Regrouping (carrying) is used in addition. When a column adds to \(10\) or more, write the ones digit and carry \(1\) to the next column on the left, because \(10\) ones make \(1\) ten, \(10\) tens make \(1\) hundred and \(10\) hundreds make \(1\) thousand.
Trading (sometimes called borrowing) is used in subtraction. When the top digit is smaller than the digit below it, take \(1\) from the next column on the left and turn it into \(10\) of the column you are working on. If that column is \(0\), keep moving left until you reach a digit you can trade from.
Addition and subtraction are inverse operations: one undoes the other. You can check a subtraction by adding, and find a missing number in an addition by subtracting. To make the largest four-digit number from four digits, put them in order from biggest to smallest (\(8, 0, 5, 2\) gives \(8520\)). For the smallest, order them from smallest to biggest, but a four-digit number cannot start with \(0\), so start with the smallest digit that is not \(0\) (\(2058\)).
These place value facts tell you when to regroup or trade, and how to check your answer.
How to add four-digit numbers
- Estimate first. Round each number to the nearest 100 or 1000 so you know roughly what the answer should be.
- Line up the places. Thousands under thousands, hundreds under hundreds, tens under tens, ones under ones. To add three numbers, line up all three by their ones digits and add each column the same way.
- Add from the ones. If a column makes \(10\) or more, write the ones digit and carry \(1\) to the next column on the left.
- Compare with your estimate. The exact answer should be close to it.
How to subtract four-digit numbers
- Put the bigger number on top and line up the places.
- Subtract from the ones. If the top digit is smaller, trade \(1\) from the next column on the left. Cross it out and write one less, and add \(10\) to the column you are working on.
- Trade across zeros. If the next column is \(0\), move left to the first digit you can trade from; each \(0\) on the way becomes \(9\).
- Check by adding. Add your answer to the number you took away. You should get the top number.
| \(\text{ones: }2 + 5\) | \(=\) | \(7\) |
| \(\text{tens: }3 + 5\) | \(=\) | \(8\) |
| \(\text{hundreds: }1 + 6\) | \(=\) | \(7\) |
| \(\text{thousands: }4 + 2\) | \(=\) | \(6\) |
No column reaches \(10\), so \(4132 + 2655 = 6787\).
| \(\text{ones: }8 + 6\) | \(=\) | \(14\ (\text{carry }1)\) |
| \(\text{tens: }6 + 4 + 1\) | \(=\) | \(11\ (\text{carry }1)\) |
| \(\text{hundreds: }7 + 5 + 1\) | \(=\) | \(13\ (\text{carry }1)\) |
| \(\text{thousands: }1 + 2 + 1\) | \(=\) | \(4\) |
Three columns regroup. \(1768 + 2546 = 4314\).
| \(\text{ones: }12 - 8\) | \(=\) | \(4\ (\text{traded 1 ten})\) |
| \(\text{tens: }14 - 6\) | \(=\) | \(8\ (\text{traded 1 hundred})\) |
| \(\text{hundreds: }3 - 1\) | \(=\) | \(2\) |
| \(\text{thousands: }7 - 3\) | \(=\) | \(4\) |
\(2\) ones is less than \(8\), so trade a ten; then \(4\) tens is less than \(6\), so trade a hundred. \(7452 - 3168 = 4284\).
| \(6000\) | \(\to\) | 5 thousands, 9 hundreds, 9 tens, 10 ones |
| \(\text{ones: }10 - 7\) | \(=\) | \(3\) |
| \(\text{tens: }9 - 4\) | \(=\) | \(5\) |
| \(\text{hundreds: }9 - 3\) | \(=\) | \(6\) |
| \(\text{thousands: }5 - 2\) | \(=\) | \(3\) |
There are no ones, tens or hundreds to trade from, so trade from the thousands: \(6000\) becomes \(5\) thousands, \(9\) hundreds, \(9\) tens and \(10\) ones. \(6000 - 2347 = 3653\).
| \(3815\) | \(\to\) | \(3800\) |
| \(2390\) | \(\to\) | \(2400\) |
| \(3800 + 2400\) | \(=\) | \(6200\) |
| \(3815 + 2390\) | \(=\) | \(6205\) |
The exact answer \(6205\) is close to the estimate \(6200\), so it is reasonable.
| \(3578 + 4673\) | \(=\) | \(8251\) |
Adding the answer to the number taken away gives back \(8251\), so Ava is correct.
| \(\square\) | \(=\) | \(8000 - 3725\) |
| \(8000 - 3725\) | \(=\) | \(4275\) |
| \(4275 + 3725\) | \(=\) | \(8000\) |
Subtraction undoes addition. The missing number is \(4275\).
| \(\text{ones: }2 + 6\) | \(=\) | \(8\) |
| \(\text{tens: }5 + 2\) | \(=\) | \(7\) |
| \(\text{hundreds: }6 + 4\) | \(=\) | \(10\ (\text{carry }1)\) |
| \(\text{thousands: }3 + 1 + 1\) | \(=\) | \(5\) |
The tens need \(5 + 2 = 7\). The hundreds must end in \(0\), so \(6 + 4 = 10\), and the carried \(1\) makes the thousands \(5\). So \(3652 + 1426 = 5078\).
| \(2486 + 315\) | \(=\) | \(2801\) |
| \(2801 - 1240\) | \(=\) | \(1561\) |
Add the new books, then subtract the books lent out: \(1561\) books are on the shelves.
Common pitfalls
Frequently asked questions
How do you add four-digit numbers?
Line up the thousands, hundreds, tens and ones. Add the ones first, then the tens, hundreds and thousands. Whenever a column makes \(10\) or more, write the ones digit and carry \(1\) to the next column on the left.
What is trading in subtraction?
Trading means taking \(1\) from the next column on the left and turning it into \(10\) in the column you are working on. You trade when the top digit is smaller than the digit you are taking away.
How do you subtract from a number with zeros, like 6000?
Trade from the first digit that is not zero. \(6000\) becomes \(5\) thousands, \(9\) hundreds, \(9\) tens and \(10\) ones, and then you can subtract each column.
How can you check a subtraction?
Add your answer to the number you took away. If you get back the starting number, the subtraction is correct. For \(6342 - 2718 = 3624\), check that \(3624 + 2718 = 6342\).
How do you estimate with four-digit numbers?
Round each number to the nearest 100 or 1000, then add or subtract the rounded numbers. For \(3815 + 2390\), \(3800 + 2400 = 6200\), so the answer should be about \(6200\).
How do you find a missing number in an addition?
Use the inverse. For \(\square + 3725 = 8000\), subtract: \(8000 - 3725 = 4275\). Then check that \(4275 + 3725 = 8000\).