Perform long division with detailed step-by-step solutions. Learn the division algorithm with clear explanations.
Basic: 84 ÷ 4
With remainder: 127 ÷ 5
Larger: 1234 ÷ 12
Three-digit: 456 ÷ 23
Perfect: 144 ÷ 12
Complex: 9876 ÷ 34
How many times does 12 go into 15? Once.
12 × 1 = 12. Write it below.
15 − 12 = 3. Must be less than 12.
Bring down the 6 to get 36. Repeat.
Long division breaks a big division problem into bite-sized steps. You work left to right through the dividend, one digit at a time, using a four-step cycle:
That's it. Four steps on a loop until you run out of digits. The number sitting on top of the bracket is your quotient, and whatever's left at the bottom is the remainder.
Division Terms:
Formula:
Divide resources equally among groups - splitting 150 books among 12 classrooms, distributing 240 candies to 15 children, or sharing costs.
Calculate unit prices (cost per item), fuel efficiency (miles per gallon), or speed (distance per hour) using division.
Divide total work hours into shifts, allocate project time across days, or determine how many items can be completed per hour.
Reduce recipe portions by dividing ingredient amounts, calculate servings per batch, or determine portions per person.
Calculate how many tiles fit in a room, how many boards can be cut from lumber, or partition materials across multiple projects.
Forgetting to bring down the next digit
After subtracting, always bring down the next digit from the dividend before continuing. Skipping this step leads to wrong answers.
Placing digits in the wrong position
Each quotient digit must align above the last digit of the portion being divided. Misalignment causes place value errors.
Incorrect subtraction
Double-check subtraction at each step. A small error early in the process propagates through all remaining steps.
Not checking the answer
Always verify: (divisor × quotient) + remainder should equal the original dividend. This catches mistakes immediately.
Best Practice
Follow the division algorithm systematically: Divide → Multiply → Subtract → Bring Down → Repeat. Check your work at the end.
| Method | Best For | Advantages | Limitations |
|---|---|---|---|
| Long Division | Any division problem, especially large numbers | Works for all cases; systematic; shows detailed steps | Time-consuming; requires careful tracking |
| Short Division | Single-digit divisors; mental math | Faster than long division; less writing required | Only practical for small divisors; harder to track steps |
| Chunking (Partial Quotients) | Learning division; building number sense | Intuitive; flexible; emphasizes understanding | Less efficient; more steps than long division |
| Repeated Subtraction | Very small numbers; understanding division concept | Shows division as repeated removal; conceptually clear | Extremely slow for large numbers; impractical |
The remainder represents what's "left over" after division when the dividend doesn't divide evenly by the divisor. Remainders can be expressed in multiple ways depending on the context.
Standard form showing quotient and remainder separately. Used when you need whole numbers only.
Remainder becomes the numerator over the divisor. Exact representation as a mixed number.
Continue division with decimal places. Most precise for measurements and calculations.
Choosing the Right Form: Use integer remainders for discrete items (people, objects), fractions for parts of wholes (recipes, measurements), and decimals for precision (money, science).