Year 3 Maths Subtraction

Subtract two-digit numbers - no regrouping

Q: How do you check a subtraction answer?

Add the answer back to the number you took away. If 78 minus 26 is 52, then 52 plus 26 should equal 78. If it does, the subtraction is correct.

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Theory

Subtracting two-digit numbers with no regrouping is a Year 3 maths skill: split each number into tens and ones, then take the ones from the ones and the tens from the tens. This page shows the column method, the split strategy and counting back on a number line, and explains what "no regrouping" means. Curriculum: VC2M3N04 / AC9M3N03.

A two-digit number is built from tens and ones. To subtract is to take one number away from another. The answer is called the difference.

With no regrouping, you never have to borrow from the next column. This happens when the top ones digit is bigger than or the same as the bottom ones digit, so each column can be subtracted on its own. In $59 - 34$ the ones give $9 - 4 = 5$ and the tens give $5 - 3 = 2$, so the difference is $25$.

Two easy ways to do it: the column method lines the numbers up and subtracts each column, and the split strategy subtracts the tens and the ones separately, then adds the parts back together.

Line the columns up, then subtract each one: $59 - 34 = 25$.

Counting back on a number line: $65 - 23 = 42$.

Subtraction has no formula, but these facts help with every question in this topic.

\[ 96 - 3 = 93 \]

96 - 3 = 93

\[ 87 - \square = 52 \]

87 - □ = 52

\[ 52 + 35 = 87 \]

52 + 35 = 87

          Taking away a one-digit number. Only the ones change: \(96 - 3 = 93\). With no regrouping, you can take away any one-digit number up to the ones digit. From \(46\) you can take \(0\) to \(6\) with no regrouping, but \(46 - 8\) needs regrouping because \(8\) is more than the \(6\) ones.
        

          Missing numbers. In \(87 - \square = 52\), the box is the amount taken away. Find it with \(87 - 52 = 35\), then check: \(52 + 35 = 87\).
        

          Stories with two steps. Write the number sentence first: start number, minus the amount taken away. Then do one subtraction at a time. Ben has \(89\) marbles. He gives away \(23\), then \(41\): \(89 - 23 = 66\), then \(66 - 41 = 25\).
        

How to subtract two-digit numbers with no regrouping

Line them up. Write the numbers with ones under ones and tens under tens.
Subtract the ones. Take the bottom ones digit from the top ones digit.
Subtract the tens. Take the bottom tens digit from the top tens digit, then read the two answers together.

          Check your ones first. If the top ones digit is bigger than or the same as the bottom ones digit, no regrouping is needed and you can subtract straight down each column.
        

Example 1 — Column method

Work out $76 - 42$.

Solution

$\text{Ones}$	$:$	$6 - 2 = 4$
$\text{Tens}$	$:$	$7 - 4 = 3$
$76 - 42$	$=$	$34$

76 - 42 = 34

The difference is $34$.

Example 2 — Split strategy

Work out $89 - 47$ by subtracting the tens and the ones separately.

Solution

$80 - 40$	$=$	$40$
$9 - 7$	$=$	$2$
$40 + 2$	$=$	$42$

89 - 47 = 42

So $89 - 47 = 42$.

Example 3 — Count back on a number line

Use a number line to find $78 - 26$.

Solution

$78 - 20$	$=$	$58$
$58 - 6$	$=$	$52$

78 - 26 = 52

Jump back $20$ then $6$, so $78 - 26 = 52$.

Example 4 — Money problem

Zoe has $\$95$. She spends $\$52$ on a jumper. How much money does she have left?

Solution

$90 - 50$	$=$	$40$
$5 - 2$	$=$	$3$
$40 + 3$	$=$	$43$

95 - 52 = 43

Zoe has $\$43$ left.

Common pitfalls

Line the columns up. Watch out for writing the digits crooked. Ones must sit under ones and tens under tens, or you will subtract the wrong digits.

Take the bottom from the top. In $59 - 34$ the ones give $9 - 4 = 5$, never $4 - 9$. Always start from the top number.

Tens still mean tens. The tens column of $59 - 34$ is $50 - 30 = 20$, so the answer is $25$, not $7$.

Frequently asked questions

How do you subtract two-digit numbers?

Line up the numbers so ones sit under ones and tens under tens. Subtract the ones first, then subtract the tens. For $59 - 34$ the ones give $9 - 4 = 5$ and the tens give $5 - 3 = 2$, so the answer is $25$.

What does no regrouping mean in subtraction?

No regrouping means you never have to borrow from the next column. It happens when the top ones digit is bigger than or equal to the bottom ones digit, so each column can be subtracted on its own.

What is the split strategy for subtraction?

The split strategy subtracts the tens and the ones separately, then adds the parts back together. For $89 - 47$ you work out $80 - 40 = 40$ and $9 - 7 = 2$, then $40 + 2 = 42$.

How do you know if you need to regroup or borrow?

Look at the ones column. If the top ones digit is smaller than the bottom ones digit, you need to regroup. If the top ones digit is bigger or the same, no regrouping is needed.

What does difference mean in maths?

The difference is the answer to a subtraction. It tells you how much is left, or how much bigger one number is than another. The difference of $76$ and $42$ is $34$.

How do you check a subtraction answer?

Add the answer back to the number you took away. If $78 - 26 = 52$, then $52 + 26$ should equal $78$. If it does, the subtraction is correct.

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Mental strategies for subtraction

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Subtract two-digit numbers - with regrouping

\(\text{Ones}\)	\(:\)	\(6 - 2 = 4\)
\(\text{Tens}\)	\(:\)	\(7 - 4 = 3\)
\(76 - 42\)	\(=\)	\(34\)

\(80 - 40\)	\(=\)	\(40\)
\(9 - 7\)	\(=\)	\(2\)
\(40 + 2\)	\(=\)	\(42\)

\(78 - 20\)	\(=\)	\(58\)
\(58 - 6\)	\(=\)	\(52\)

\(90 - 50\)	\(=\)	\(40\)
\(5 - 2\)	\(=\)	\(3\)
\(40 + 3\)	\(=\)	\(43\)

Subtract two-digit numbers - no regrouping

📖 Theory

How to subtract two-digit numbers with no regrouping

Common pitfalls

Frequently asked questions

Theory