Math Order Arena — Learn the Rules Game

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Math Order Arena

Learn the rule, choose the answer, understand the reason.

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THE RULES ARE THE GAME

Math has a turn order.

Treat every expression like a game. Parentheses play first, then powers, then multiplication/division, then addition/subtraction. When two operations have the same rank, move from left to right.

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Core rule

() → xⁿ → ×÷ → +−

Same priority? Solve left to right.

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Question 1 of 12

Order of operations

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8 + 2 × 3

What is the correct result?

Correct!

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Round complete!

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Rules of the math game

Imagine each operation is a player waiting for its turn. The higher-priority player goes first.

1

Parentheses / grouping Solve what is grouped first. A fraction bar also groups its numerator and denominator.

2

Powers and roots Evaluate exponents and roots before multiplication, division, addition or subtraction.

3

Multiplication and division They have equal priority. If both appear, calculate from left to right.

4

Addition and subtraction They also have equal priority. Work from left to right.

5

Special definitions Examples: a nonzero number to the power 0 equals 1; division by zero is undefined.

6

Infinite processes For infinite sums and limits, ask whether the process converges before trying to assign a finite answer.

Why this order?

Why multiplication before addition?

Multiplication is repeated scaling/grouping. The convention keeps expressions unambiguous: 2 + 3 × 4 means 2 + (3 × 4), not (2 + 3) × 4.

Why left to right?

Multiplication and division share the same rank; addition and subtraction share the same rank. Left-to-right breaks the tie consistently.

What does a fraction bar mean?

The bar is grouping. Finish the whole numerator and whole denominator first, then divide.

What about 0 powers?

For any nonzero a, a⁰ = 1. This preserves exponent laws such as a³/a³ = a³⁻³ = a⁰ = 1.

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