Subtraction
Take away to find the difference · 뺄셈
1. What Is Subtraction?
Subtraction finds the difference between two numbers — how much is left after taking one away, or how far apart two values are. In a − b, the number a is the minuend, b is the subtrahend, and the result is the difference.
Subtraction is the exact inverse of addition: if a + b = c, then c − b = a. That relationship is the key to checking your work and to the fastest mental strategies.
뺄셈은 두 수의 차이를 구합니다 — 빼고 남은 양, 또는 두 값의 거리입니다. a − b에서 a를 피감수(minuend), b를 감수(subtrahend)라 합니다. 뺄셈은 덧셈의 역(a + b = c ⇒ c − b = a)으로, 검산과 암산의 핵심입니다.
2. The Column Algorithm & a Worked Example
Align the numbers by place value and subtract each column right to left. When the top digit is smaller than the bottom one, borrow 10 from the next column to the left.
Worked example. Subtract 503 − 178:
- Ones: 3 − 8 won’t go. Borrow from the tens — but the tens digit is 0, so borrow from the hundreds first (5 → 4), making the tens 10; then the tens lend to the ones (10 → 9), making the ones 13. Now 13 − 8 = 5.
- Tens: 9 − 7 = 2.
- Hundreds: 4 − 1 = 3.
So 503 − 178 = 325. Check by addition: 325 + 178 = 503. ✓
자릿값을 맞춰 오른쪽부터 빼고, 위 숫자가 작으면 왼쪽에서 10을 빌려옵니다(받아내림). 예: 503 − 178에서 0을 가로질러 빌려 13−8=5, 9−7=2, 4−1=3 → 325. 검산: 325 + 178 = 503.
3. Faster Mental Strategies
Borrowing is error-prone in your head. Two shortcuts avoid it entirely:
- Counting up. Treat a − b as “what plus b makes a?” For 503 − 178: 178 → 180 (+2) → 200 (+20) → 500 (+300) → 503 (+3). Total stepped up: 2 + 20 + 300 + 3 = 325.
- Equal addition. Add the same amount to both numbers (the difference is unchanged): 503 − 178 = 525 − 200 = 325.
암산에서는 받아내림 대신 더해가기(178에서 503까지 올라가며 더한 양 = 325)나 같은 수 더하기(525 − 200 = 325)가 깔끔합니다.
4. Key Properties
- Not commutative. a − b ≠ b − a in general (5 − 3 = 2 but 3 − 5 = −2).
- Not associative. (a − b) − c ≠ a − (b − c) in general.
- Identity on the right. a − 0 = a, and a − a = 0.
- Inverse of addition. a − b = a + (−b); subtracting is adding the opposite.
뺄셈은 교환법칙·결합법칙이 성립하지 않습니다(a − b ≠ b − a). a − 0 = a, a − a = 0이며, a − b = a + (−b)로 음수를 더하는 것과 같습니다.
5. Frequently Asked Questions
How do you subtract with borrowing? Subtract right to left; whenever the top digit is too small, borrow 10 from the next column left (reducing that column by 1) and continue.
How do you subtract across a zero? Keep borrowing leftward until you reach a non-zero digit; each zero you pass becomes a 9 after lending onward.
Is subtraction commutative? No. a − b and b − a are negatives of each other, so order matters.
오른쪽부터 빼되 위 숫자가 작으면 왼쪽에서 10을 빌립니다. 0을 가로지를 때는 0이 아닌 자리까지 계속 빌리며, 거친 0들은 9가 됩니다. 뺄셈은 교환법칙이 성립하지 않습니다.
Ready to practice? Drill subtraction and the other operations on C:Arith, or review the full arithmetic reference and the related addition, multiplication, and division.