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Order of operations
Brackets, powers, multiply/divide, add/subtract — and why the order is not optional.
An expression like 3 + 4 × (2 − 1)² has only one correct value because everyone agrees on the order: brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. The animation below performs exactly one operation per step, in that order.
Ví dụ đã làm: 3 + 4 * (2 - 1)^2
Bước một bước
- 3 + 4 \left(-1 + 2\right)^{2} = 7
Add: -1 + 2 = 1.
Giải đáp
Symbols used here
Inequalities that allow equality; < and > exclude it.
Both signs at once: x = 3 ± 2 means 5 and 1.
The two sides are different.
Equal to the precision shown, not exactly.
The non-negative number whose square (n-th power) is x.
What is left after dividing a by n.
Per hundred: 15% = 15/100.
a for every b; a divided by b.
How to: Order of operations
- Add: -1 + 2 = 1.
Questions people ask
Why does the order of operations matter?
Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.
How do I check an arithmetic answer?
Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.
Why are fractions harder than decimals?
They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.