How Long Division Works
Long division breaks a division problem into a sequence of easier steps. For each digit of the dividend, you repeat four steps: Divide, Multiply, Subtract, Bring Down.
Step-by-Step Process
- Divide: How many times does the divisor go into the current number?
- Multiply: Multiply the divisor by that quotient digit
- Subtract: Subtract the product from the current number
- Bring down: Bring down the next digit of the dividend
- Repeat until all digits have been used. The final subtraction result is the remainder.
Example: 100 ÷ 7
- 7 goes into 10 = 1 time. 1 × 7 = 7. Subtract: 10 − 7 = 3.
- Bring down 0 → 30. 7 goes into 30 = 4 times. 4 × 7 = 28. Subtract: 30 − 28 = 2.
- No more digits. Quotient = 14, Remainder = 2.
Ways to Express Division Results
| Format | Example (100 ÷ 7) | When to Use |
|---|---|---|
| Quotient + Remainder | 14 R2 | Elementary math, whole number contexts |
| Mixed Fraction | 14 2/7 | Exact representation, fractions work |
| Decimal | 14.285714... | Scientific, financial calculations |
Checking Your Answer
To verify: (Quotient × Divisor) + Remainder = Dividend
For 100 ÷ 7 = 14 R2: (14 × 7) + 2 = 98 + 2 = 100
Division Terminology
- Dividend: The number being divided (100)
- Divisor: The number dividing into it (7)
- Quotient: The result of division (14)
- Remainder: The leftover amount (2)
Division Rules
- Any number divided by 1 equals itself
- Any number divided by itself equals 1
- Zero divided by any number equals 0
- Division by zero is undefined
- Negative ÷ positive = negative; negative ÷ negative = positive