Arithmetic | 6 of 17
Prerequisites: Addition, Multiplication. Enables: Algebra.
Order of operations gives a consistent way to evaluate expressions.
Use this sequence:
Parentheses and grouping symbols
Exponents and roots
Multiplication and division from left to right
Addition and subtraction from left to right
A common memory aid is PEMDAS, but multiplication and division have equal priority. Addition and subtraction also have equal priority.
Grouping symbols
Evaluate inside grouping symbols first.
Common grouping symbols:
$$
(\ ),\quad [\ ],\quad \{\ \}
$$
Example:
$$
3(4+5)=3(9)=27
$$
Without parentheses:
$$
3\cdot4+5=12+5=17
$$
Left-to-right rule
For operations with equal priority, work left to right.
Example:
$$
24 \div 6 \times 2
$$
Evaluate left to right:
$$
24 \div 6 = 4
$$
$$
4 \times 2 = 8
$$
Therefore:
$$
24 \div 6 \times 2 = 8
$$
Nested expressions
Example:
$$
2[3^2 + (12-5)]
$$
First:
$$
3^2 = 9
$$
and
$$
12 - 5 = 7
$$
Then:
$$
2[9+7] = 2[16] = 32
$$
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