What Is Difference In Math? Meaning, Methods And Examples
The short version
- The difference in math is the answer to a subtraction problem. In 10 – 4 = 6, the difference is 6.
- “Find the difference between two numbers” means subtract the smaller from the larger. It tells you how far apart the numbers are.
- You can find a difference by taking away or by counting up from the smaller number. Counting up is often faster for problems like 1,000 – 764.
- The parts of a subtraction problem are the minuend (the starting number), the subtrahend (the number taken away) and the difference.
- Check any difference by adding it back: the difference plus the smaller number should equal the larger number.
The difference in math is the result you get when you subtract one number from another. The difference between 15 and 9 is 6, because 15 – 9 = 6. It tells you how much bigger one number is than another, or how far apart they sit on a number line.
When homework says “find the difference,” it’s asking for subtraction. Below we’ll cover the vocabulary, two ways to think about difference, how it works with decimals, fractions and negative numbers, the mistakes that show up most, and practice problems with an answer key.
What is difference in math? The vocabulary
Every subtraction problem has three parts:
18 – 11 = 7
18 is the minuend (the amount you start with)
11 is the subtrahend (the amount you subtract)
7 is the difference (the result)
Most kids never need “minuend” and “subtrahend” outside a vocabulary quiz. “Difference” is the word that matters, because it shows up in word problems constantly. It sits alongside the names for the other three operations:
| Operation | Name of the answer | Example |
|---|---|---|
| Addition | Sum | 6 + 2 = 8 |
| Subtraction | Difference | 6 – 2 = 4 |
| Multiplication | Product | 6 × 2 = 12 |
| Division | Quotient | 6 ÷ 2 = 3 |
Word problems use lots of phrases that mean “find the difference”: how many more, how many fewer, how much less, how much longer, how much is left, how far apart, and what’s the change.
Two ways to find a difference
Take away
This is the version most kids learn first. Start with the larger amount and remove the smaller one. If you have 9 crackers and eat 4, you have 9 – 4 = 5 left. Take away works well when the number being subtracted is small.
Count up (think of distance)
Here you ask, “How far is it from the smaller number to the bigger one?” This is the more powerful idea, and it’s why the word “difference” fits: the difference in math is really a distance. The difference between 764 and 1,000 is the distance between them on a number line.
Example: 1,000 – 764
764 up to 800 is 36
800 up to 1,000 is 200
36 + 200 = 236
So 1,000 – 764 = 236.
Compare that with regrouping across three zeros, which is where many kids lose track. Counting up avoids the problem entirely. When the two numbers are close together, like 503 and 497, counting up is almost always faster too: 497 to 500 is 3, and 500 to 503 is 3 more, so the difference is 6.
A bonus trick: shift both numbers
If you add the same amount to both numbers, the difference doesn’t change. That’s because you’re just sliding both points along the number line together.
82 – 39
Add 1 to both: 83 – 40
83 – 40 = 43
Worked examples of difference
Whole numbers with regrouping. 503 – 278
Ones: 3 is less than 8, and the tens place is 0, so regroup from the hundreds. 503 becomes 4 hundreds, 9 tens, 13 ones.
13 – 8 = 5, 9 – 7 = 2, 4 – 2 = 2
Difference: 225. Check: 278 + 225 = 503.
Decimals. 5.2 – 3.75
Line up the decimal points and write 5.2 as 5.20.
5.20 – 3.75 = 1.45
Check: 3.75 + 1.45 = 5.20.
Fractions. 3/4 – 1/3
Common denominator is 12: 3/4 = 9/12 and 1/3 = 4/12.
9/12 – 4/12 = 5/12
Negative numbers. What’s the difference between 6 and -4?
6 – (-4) = 6 + 4 = 10
On a number line, -4 is 4 steps below zero and 6 is 6 steps above it, so they’re 10 apart.
Temperature. It was -3°F in the morning and 8°F in the afternoon. How much did it warm up?
8 – (-3) = 11 degrees.
Is the difference always positive?
When a problem asks for “the difference between” two numbers, it almost always wants the distance between them, which is positive. The difference between 3 and 10 is 7, no matter which one is named first.
Once kids reach algebra, it gets more precise. “The difference of a and b” usually means a – b, in that order, and that can come out negative: 3 – 10 = -7. If you want the distance no matter the order, you use absolute value: |3 – 10| = 7. So for elementary word problems, subtract smaller from larger. In middle school, pay attention to the order the problem gives you.
Common mistakes with difference
- Subtracting the smaller digit from the larger in every column. On 52 – 38, a kid might do 8 – 2 = 6 in the ones and 5 – 3 = 2 in the tens, and write 26. The real answer is 14. This mistake means the kid doesn’t yet see why regrouping is needed.
- Getting lost regrouping across zeros. Problems like 400 – 157 (answer: 243) are where regrouping breaks down most. Counting up is a good backup method.
- Adding when the problem says “difference.” Kids skim for numbers and default to adding. Teaching the answer names (sum, difference, product, quotient) helps.
- Flipping the order with “less than.” “5 less than 12” is 12 – 5, not 5 – 12. In algebra, “5 less than x” is x – 5.
- Misaligned decimals. Writing 5.2 – 3.75 with the digits right-aligned instead of the decimal points lined up gives nonsense. Adding a zero (5.20) fixes it.
Practice problems
- What’s the difference in 15 – 8?
- Find the difference between 64 and 29.
- 700 – 346 = ?
- Maya has 142 cards. Leo has 87. How many more cards does Maya have?
- 8.4 – 2.65 = ?
- 5/6 – 1/4 = ?
- What’s the difference between 12 and -5?
- Two numbers have a sum of 50 and a difference of 14. What are the numbers?
Answers
- 7.
- 64 – 29 = 35. (Shift trick: 65 – 30 = 35.)
- 354. Count up: 346 to 350 is 4, 350 to 700 is 350, and 4 + 350 = 354.
- 142 – 87 = 55 more cards.
- 8.40 – 2.65 = 5.75.
- 10/12 – 3/12 = 7/12.
- 12 – (-5) = 17.
- 32 and 18. Add the sum and difference and halve it: (50 + 14) ÷ 2 = 32. Then 50 – 32 = 18. Check: 32 – 18 = 14.
If your kid is stuck on difference, look for an earlier gap
A kid who struggles with difference in math usually has a place value gap underneath. Regrouping only makes sense if you know that 5 tens can become 4 tens and 10 ones. When that idea is shaky, kids memorize the borrowing steps and then drop them the moment a zero shows up. Addition and subtraction facts to 20 are the other usual suspect: if 13 – 8 takes finger counting, every multi-digit problem gets slow and error-prone. Our guide to math skills by grade level shows where these skills normally land.
Slow, careful subtraction can also look like a kid who “hates math” when it’s really a kid who’s tired of getting things wrong. If homework has started to bring tears, math anxiety in children is worth reading. And short daily practice does more for fact fluency than long weekend sessions, as we explain in why 20 minutes a day works.
Frequently asked questions
In math, what is difference?
It’s the result of subtraction. The difference between two numbers is how much larger one is than the other.
What does “find the difference” mean?
It means subtract. Take the larger number minus the smaller number to find how far apart they are.
What’s the difference between sum and difference?
A sum is the answer to an addition problem. A difference is the answer to a subtraction problem. For 9 and 3, the sum is 12 and the difference is 6.
Can a difference be negative?
Yes, when order matters. 4 – 9 = -5. But “the difference between 4 and 9” in an elementary word problem usually means the distance, which is 5.
What’s the difference of two equal numbers?
Zero. Any number minus itself is 0, since there’s no distance between them.
Find the actual gap
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