Perform long division with quotient and remainder, mixed fractions, recurring decimal detection, and complete step-by-step visual division tableaus.
Division is one of the four fundamental operations of arithmetic (alongside addition, subtraction, and multiplication). It represents the mathematical process of splitting a quantity into equal parts or determining how many times one number is contained within another.
Division is the inverse operation of multiplication. For instance, if $4 \times 3 = 12$, then $12 \div 3 = 4$ and $12 \div 4 = 3$.
The total quantity or number that is being divided into groups. (Inside the bracket).
The number of parts or size of groups dividing the dividend. (Left of the bracket).
The resulting whole number of times the divisor fits into the dividend. (Above the bar).
The leftover amount that cannot be evenly divided (0 ≤ r < d).
| Notation Style | Example | Usage Context |
|---|---|---|
| Obelus / In-Line Symbol | 100 ÷ 7 | Standard arithmetic notation in elementary math and calculators. |
| Solidus / Slash | 100 / 7 | Common in programming languages, web URLs, and inline text. |
| Horizontal Fraction Bar | 100/7 | Standard in algebra and advanced mathematics. |
| Long Division Bracket | 7 ) 100 | Traditional manual long division tableau format. |
Take the whole quotient as the whole integer part, place the remainder over the divisor as the fractional part, and simplify the fraction if possible: q r/d (e.g. 100 ÷ 7 = 14 2/7).
A repeating decimal occurs when long division yields a remainder that has occurred previously, causing the same sequence of digits to repeat infinitely (e.g. $100 \div 7 = 14.\overline285714$).
Division by zero has no consistent mathematical meaning because no number multiplied by 0 can equal a non-zero dividend.