1Parentheses always come first, no matter what
Parentheses are a signal that says "calculate this part first." They outrank every other rule, so whenever you see parentheses in an expression, you always start inside them.
Calculate 12 + 8 = 20 inside the parentheses first, then 20 × 3 = 60.
2Multiplication/division comes before addition/subtraction
Without parentheses, multiplication and division are calculated before addition and subtraction. Calculate in the wrong order and you get a completely different answer.
Calculate 8 × 3 = 24 first, then 12 + 24 = 36 is the correct answer. (Doing 12 + 8 first gives 60, which is wrong!)
3Same-priority operations go left to right
Multiplication and division share the same priority, and so do addition and subtraction. When there are several operations at the same priority, calculate the one on the left first, in order.
Multiplication isn't specially first over division — you calculate the leftmost one, 6 × 4 = 24, first, then 24 ÷ 2 = 12.
4Putting it all together
Follow just these three steps in order, and no matter how complicated the expression, you'll always get one correct answer.
5Try this
- Calculate the same numbers in a different order. Compare the answer for "2 + 3 × 4" solved by the rule versus solved straight from the left.
- Add and remove parentheses. Check step by step why "10 - 4 + 2" and "10 - (4 + 2)" give different answers.
- In the quiz, just pick out "what to calculate first." You don't have to work out the full answer — knowing where to start is the first step.