math · 28 minutes · Official OETT Aligned
Basic Math & Order of Operations
Know which calculation to do first
What to know
- addition and subtraction
- multiplication and division
- PEMDAS: the order of operations
- checking calculator entries
Doing the right calculations in the wrong order can still give a wrong answer.
The core rule
Do parentheses first, then powers. Multiply and divide from left to right, then add and subtract from left to right.
PEMDAS reminds you of the order: Parentheses, Exponents (powers), Multiplication and Division, Addition and Subtraction. Multiplication and division have equal priority, so work left to right. Addition and subtraction also share priority. Check that your calculator follows this order; a basic calculator may work one step at a time.
Worked examples
Example 1: easy
18 − 3 × 4 = 6.
- Multiply before subtracting: 3 × 4 = 12.
- Then compute 18 − 12 = 6 and check that 6 is smaller than 18.
Multiply first, then subtract.
Example 2: medium
24 ÷ 6 + 3 × 5 = 19.
- Work division and multiplication before addition: 24 ÷ 6 = 4 and 3 × 5 = 15.
- Add the results: 4 + 15 = 19.
Finish the multiplication and division before adding.
Example 3: hard
72 − (18 ÷ 3) × 7 = 30.
- Work inside parentheses first: 18 ÷ 3 = 6.
- Multiply 6 × 7 = 42, then subtract 72 − 42 = 30.
Parentheses tell you to work out that part first.
Common mistakes
PEMDAS means always multiply before dividing.
Multiply and divide in the order you meet them from left to right.
Put it into practice
Use guided explanations, check your answers, and try a new variation.