Subtraction is the operation that finds how much is left when you take one amount away from another, or how far apart two numbers are. It is written with a minus sign: 9 − 4 = 5. The answer is called the difference. Subtraction undoes addition, so you can check 9 − 4 = 5 by adding 5 + 4 = 9.
In Spanish
resta
Also called
subtracting, take away, minus, finding the difference
Taking 4 away from 9, jumping back 4 from 9, and asking “what plus 4 makes 9?” all give the same difference, 5.
Formal definition and notation
For numbersa and b, the differencea − b is the unique number c such that b + c = a. So subtraction is an unknown-addend problem: 10 − 8 asks what to add to 8 to make 10. For all real numbers, subtracting b is the same as adding its opposite: a − b = a + (−b).
This rule makes subtraction with negative numbers routine: 5 − (−6) = 5 + 6 = 11.
Try it: difference as distance
Interactive
Drag the two points, or select one and use the arrow keys. The readout subtracts the smaller from the larger to give the distance between them. Try moving one point left of 0.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Subtraction examples, step by step
Example 1: Subtract with regrouping
Warm-up
Find 52 − 27.
Ones: 2 is less than 7, so regroup 1 ten as 10 ones: 52 becomes 4 tens and 12 ones.
Ones: 12 − 7 = 5.
Tens: 4 − 2 = 2.
Check by adding: 25 + 27 = 52.
Answer: The difference is 25.
Example 2: Subtracting negative numbers
Core
Find −3 − 8 and 5 − (−6).
Rewrite as adding the opposite: −3 − 8 = −3 + (−8).
Both numbers are negative, so move 8 left from −3: −11.
Second: 5 − (−6) = 5 + 6, because the opposite of −6 is 6.
5 + 6 = 11.
Answer:−3 − 8 = −11 and 5 − (−6) = 11.
Example 3: Temperature drop
Test-style
The temperature was 14 °F at noon and −9 °F at midnight. By how many degrees did it fall?
The drop is the higher temperature minus the lower one: 14 − (−9).
Add the opposite: 14 + 9.
14 + 9 = 23. Check on a thermometer: 14 down to 0 is 14 degrees, then 9 more to −9.
Answer: The temperature fell 23 degrees.
Common mistakes
✗ MistakeFor 52 − 27, subtract the smaller digit from the larger in each column: 7 − 2 = 5, 5 − 2 = 3, answer 35.
✓ InsteadRegroup: 12 − 7 = 5 in the ones and 4 − 2 = 2 in the tens, answer 25.
Always subtract the bottom digit from the top digit. When the top digit is smaller, borrow a ten instead of flipping the digits.
✗ Mistake5 − (−6) = −1
✓ Instead5 − (−6) = 5 + 6 = 11
Subtracting a negative means adding its opposite. Taking away a debt of 6 dollars leaves you 6 dollars better off.
✗ Mistake“7 less than 20” is 7 − 20.
✓ Instead“7 less than 20” is 20 − 7 = 13.
“Less than” reverses the order: start with 20 and take 7 away. Compare “20 minus 7”, which is written in order.
The minus sign between two numbers means subtract; a dash attached to one number makes it negative. In 8 − (−2) the first dash subtracts and the second makes negative two.
Addition combines amounts; subtraction finds what is left or the gap. They undo each other: 9 − 4 = 5 because 5 + 4 = 9.
Quick check: 3 questions
Question 1 of 3
What is 403 − 168?
Show answer and explanation
Answer: C. Regroup twice: 403 is 3 hundreds, 9 tens and 13 ones. 13 − 8 = 5, 9 − 6 = 3, 3 − 1 = 2, so 235. Check: 235 + 168 = 403. 345 and 335 come from regrouping errors, and 571 is the sum.
Question 2 of 3
What is −7 − (−10)?
Show answer and explanation
Answer: B.−7 − (−10) = −7 + 10 = 3. −17 subtracts 10 instead of adding it, −3 has the wrong sign, and 17 ignores both signs.
Question 3 of 3
Which expression means “6 fewer than a number n”?
Show answer and explanation
Answer: D. “6 fewer than n” starts with n and takes 6 away: n − 6. 6 − n is the common reversed-order mistake.
Subtraction: frequently asked questions
What are the parts of a subtraction problem called?
In 9 − 4 = 5, the 9 is the minuend (the number you start with), the 4 is the subtrahend (the amount you take away), and the 5 is the difference (the answer). Most teachers just say “the first number” and “the number being subtracted”, but the answer is always called the difference.
Can you subtract a bigger number from a smaller one?
Yes, and the answer is negative. 4 − 9 = −5: start at 4 on the number line and move 9 units left, which passes 0 and lands on −5. With whole numbers only, as in early grades, the problem has no answer, which is why young students are told they cannot do it.
How do you check a subtraction answer?
Add the difference to the number you subtracted; you should get the number you started with. For 403 − 168 = 235, check 235 + 168 = 403. This works because addition and subtraction are inverse operations, so each one undoes the other.
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