Subtract two-digit numbers - with regrouping
Theory
Subtracting two-digit numbers with regrouping is a Year 3 maths skill: subtract the ones first, and when the top ones digit is too small, trade one ten for ten ones and borrow it into the ones column. This page explains regrouping, the column method, the split strategy and the number line jump-back strategy for differences like \(64 - 27\). Curriculum: VC2M3N04 / AC9M3N03.
To subtract two-digit numbers you subtract the ones first, then the tens. Sometimes the top ones digit is too small to take the bottom one away. Then you regroup: trade 1 ten from the tens column for 10 more ones. Trading that ten across is also called borrowing.
For \(64 - 27\), the ones are \(4 - 7\), but 4 is too small. Trade 1 ten: the 4 ones become 14 and the 6 tens drop to 5. Now the ones make \(14 - 7 = 7\) and the tens make \(5 - 2 = 3\), which gives \(37\).
There is more than one way to subtract. The column method lines the digits up and subtracts each column, regrouping when needed. The split strategy renames the top number so the ones are big enough, then subtracts the tens and ones on their own. The jump-back strategy starts at the larger number on a number line and jumps back the tens, then the ones.
Regrouping rests on a few place value facts. Keep these in mind whenever the ones will not subtract.
How to subtract two-digit numbers with regrouping
- Line up the columns. Write the numbers so ones sit under ones and tens under tens.
- Subtract the ones. If the top ones digit is too small, trade 1 ten: cross out the tens digit and drop it by 1, and add 10 to the ones. Then subtract the ones.
- Subtract the tens. Take the bottom tens digit away from the tens that are left. Write the total to get your answer.
| \(\text{ones: }6 - 8\) | \(\text{too small}\) | |
| \(\text{trade }1\text{ ten: }16 - 8\) | \(=\) | \(8\) |
| \(\text{tens drop to }3\) |
So \(46 - 8 = 38\).
| \(94\) | \(=\) | \(80 + 14\) |
| \(\text{tens: }80 - 50\) | \(=\) | \(30\) |
| \(\text{ones: }14 - 8\) | \(=\) | \(6\) |
| \(30 + 6\) | \(=\) | \(36\) |
Renaming \(94\) as \(80 + 14\) makes the ones big enough, so \(94 - 58 = 36\).
| \(64 - 20\) | \(=\) | \(44\) |
| \(44 - 7\) | \(=\) | \(37\) |
Jump back \(-20\), then \(-7\) crosses \(40\): \(64 - 27 = 37\).
| \(\text{ones: }2 - 7\) | \(\text{too small}\) | |
| \(\text{trade }1\text{ ten: }12 - 7\) | \(=\) | \(5\) |
| \(\text{tens: }7 - 5\) | \(=\) | \(2\) |
The tens drop from 8 to 7 after the trade, so Ava has \(\$25\) left.
Common pitfalls
Frequently asked questions
How do you subtract two-digit numbers with regrouping?
Subtract the ones first. If the top ones digit is too small, trade 1 ten from the tens column for 10 more ones, then subtract. Remember the tens digit is now one smaller. For \(64 - 27\), the ones become \(14 - 7 = 7\) and the tens become \(5 - 2 = 3\), giving \(37\).
What does regrouping or borrowing mean in subtraction?
Regrouping means trading one ten for ten ones. When the top ones digit is smaller than the bottom one, you take 1 ten from the tens column and add 10 to the ones so you can subtract. The tens digit drops by one.
When do you need to regroup when subtracting?
You regroup whenever the top digit in a column is smaller than the digit below it. Check the ones first: if the top ones digit is smaller, you must trade a ten. For \(53 - 8\) the ones are \(3 - 8\), so you regroup.
What is the split strategy for subtraction?
The split strategy renames the top number so the ones are big enough, then subtracts the tens and ones separately. For \(94 - 58\), rename \(94\) as \(80 + 14\), then \(80 - 50 = 30\) and \(14 - 8 = 6\), so \(30 + 6 = 36\).
How do you subtract on a number line using the jump-back strategy?
Start at the larger number, then jump back the tens and the ones. For \(64 - 27\), start at \(64\), jump back \(20\) to reach \(44\), then jump back \(7\) to land on \(37\).
What is 64 - 27?
\(64 - 27 = 37\). The ones 4 cannot take 7, so trade one ten to make \(14 - 7 = 7\). The tens are now \(5 - 2 = 3\), so the answer is \(37\).