Order of Operations (Grade 5)

Order of operations is the agreed rule for which calculation to do first in an expression with more than one operation. Without it, the same expression could give different answers. In 2 + 3 × 4, adding first gives 2 + 3 = 5, then 5 × 4 = 20. Multiplying first gives 3 × 4 = 12, then 2 + 12 = 14. Math always uses the second way, so 2 + 3 × 4 = 14.

The rule is often remembered by the word PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Parentheses are solved first, no matter where they are in the expression. Exponents come next. Then multiplication and division, and last, addition and subtraction.

Multiplication and division have equal rank, and so do addition and subtraction. When an expression has only one of these pairs, work from left to right. In 20 ÷ 4 × 5, division comes first because it is on the left: 20 ÷ 4 = 5, then 5 × 5 = 25. Doing the multiplication first would give the wrong answer.

Parentheses always go first, even if the operation inside them is addition. In 3 × (4 + 1), you solve the parentheses before multiplying: 4 + 1 = 5, then 3 × 5 = 15. In (8 - 3) × 6 + 7, the parentheses go first again: 8 - 3 = 5, then 5 × 6 = 30, then 30 + 7 = 37.

To check your work, go through the same steps again in the same order and write down each result. If you get a different number the second time, you likely skipped a step or did two operations in the wrong order.

Worked examples