Order of Operations

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Order of Operations

If you want to calculate \(\frac{8+4}{2}\) and you enter \(8+4 \div 2\) into your calculator, you will get 10 instead of the correct answer, which is 6. The reason for this is that when multiple operations are involved, the calculator uses the order of operations and determines that it should first divide. To get the correct answer, the numerator needs parentheses.

The Order of Operations is as Follows

Evaluate expressions in parentheses first.
Evaluate any exponents.
Do \(\times\) and \(\div\) in the order they appear from left to right.
Do \(+\) and \(-\) in the order they appear from left to right.

Examples:

\(8 + 4 \div 2 = 8 + 2 = 10\)

\((8 + 4) \div 2 = 12 \div 2 = 6\)

*To avoid doing the calculation incorrectly, when the numerator or denominator of an expression involves more than one number, put parentheses around the group of numbers in the numerator. Then enter the \(\div\) sign. Then put parentheses around the group of numbers in the denominator.

Examples:

\(\frac{-4.02+6.04}{2-4} = (-4.02 + 6.04)\div (2 - 4)\)

\(\frac{2.578^2}{4\times (0.03)^2}=(2.578 \times 2.578) \div (4 \times 0.03 \times 0.03)\)

\(\frac{8+(2-3)(6)+(4-2)\times 10}{(8-4-2)\times 2}\)