What are the four basic arithmetic operations?
Addition (+) combines quantities, subtraction (−) finds the difference, multiplication (×) is repeated addition, and division (÷) splits into equal parts. They come in inverse pairs: subtraction undoes addition, and division undoes multiplication. All of higher mathematics builds on these four operations.
Why is division by zero undefined?
Division asks "how many times does the divisor fit into the dividend?" — and zero fits into any non-zero number infinitely many times, while 0 ÷ 0 could be any value at all. Because no single consistent answer exists, mathematics leaves division by zero undefined, and this calculator flags it rather than returning a misleading result.
What order do operations happen in a longer expression?
The standard order (PEMDAS/BODMAS) is: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). So 2 + 3 × 4 = 14, not 20. This calculator works on one operation at a time — use the "Use result" button to chain calculations in exactly the order you intend.
Why do decimal calculations sometimes show tiny rounding differences?
Computers store numbers in binary, and many decimal fractions (like 0.1) have no exact binary representation — famously, 0.1 + 0.2 = 0.30000000000000004 in raw floating point. This calculator rounds results to 12 significant digits, which removes this artefact for everyday calculations.
Why do people get different answers for expressions like 6 divided by 2(1+2)?
Because the notation is genuinely ambiguous, not because one side is bad at arithmetic. Everyone agrees the bracket resolves first, giving 6 divided by 2 times 3. The disagreement is over whether implied multiplication — a number written directly against a bracket — binds more tightly than the division sign. Many hand-written mathematical and scientific conventions treat it as tighter, giving 1; most calculators and programming languages apply plain left-to-right precedence, giving 9. There is no hidden correct answer to discover. The lesson is a practical one: write the brackets you mean, and the ambiguity disappears.
When should division give a remainder instead of a decimal?
Whenever the thing being divided cannot be split. Seventeen people into cars holding five each is not 3.4 cars; it is three full cars and two people left over, so you need four. Dividing 17 by 5 with a remainder gives quotient 3 and remainder 2, which is the answer that reflects reality. The same applies to boxes, bus seats, tiles from a pack and pages in a print run — all cases where you round up rather than to the nearest. Decimal division is the right tool when the quantity really is continuous, such as sharing a length of rope or a sum of money.