Results
Long division layout
How it’s calculated
Shortcuts: Alt+S share, Alt+L copy LaTeX, Alt+[ previous step, Alt+] next step.
Teacher notes
- Before dividing, decimals are turned into whole numbers by multiplying by 10 or 100, then every subtraction and remainder is logged for the class.
- Highlight colours match the digits in the written layout, so students can follow “what we are looking at” and “what we subtract” more easily.
Worked examples & quick checks
Remainder vs decimal
Many school problems want a quotient with a remainder (e.g., 127 ÷ 5 = 25 remainder 2). If you need decimal digits, increase “Max decimal digits” and the calculator will continue the division past the decimal point.
Examples
- 127 ÷ 5: quotient 25, remainder 2. With one decimal digit, it becomes 25.4 (because 2/5 = 0.4).
- 1 ÷ 3: 0.333… is repeating. The calculator detects repeats by tracking remainders while generating digits.
- 22 ÷ 7: 3.142857142857… is repeating. Use a larger “Max decimal digits” to see more of the repeating cycle.
- 1.2 ÷ 0.3: this is the same as 12 ÷ 3, so the exact quotient is 4 (no remainder).
Quick checks & tips
- Check your work: dividend = divisor × quotient + remainder (with 0 ≤ remainder < |divisor| for whole-number division).
- Negative numbers: divide the absolute values, then apply the sign rule (− ÷ + = −, − ÷ − = +).
- Rounding: if you stop at N decimal digits, the result is a truncated/rounded approximation. If an exact fraction form is needed, keep the remainder answer.
References
FAQ
What is a remainder?
The remainder is the amount left over after dividing. If the remainder is 0, the dividend is exactly divisible by the divisor.
How do I get a decimal answer instead of a remainder?
Increase “Max decimal digits” above 0 to continue the division past the decimal point. For many school problems you will be asked to give a quotient with a remainder instead.
How does the calculator detect repeating decimals?
While generating decimal digits, the tool stores each remainder it sees. When the same remainder appears again, the digits from that point form a repeating pattern.