BIDMAS, BODMAS and PEMDAS: the order of operations explained

The order of the letters makes it look as if division always comes before multiplication (BIDMAS) or multiplication before division (PEMDAS). That's not the rule. Multiplication and division have equal priority, and so do addition and subtraction: work them from left to right.

• $12 \div 3 \times 2 = 4 \times 2 = 8$ (not $12 \div 6 = 2$)
• $10 - 4 + 1 = 6 + 1 = 7$ (not $10 - 5 = 5$)

1. $3 + 4 \times 2 = 3 + 8 = 11$
2. $(3 + 4) \times 2 = 7 \times 2 = 14$
3. $20 - 2 \times 3^2 = 20 - 2 \times 9 = 20 - 18 = 2$
4. $\dfrac{8 + 4}{2 \times 3} = \dfrac{12}{6} = 2$ (a fraction bar acts like brackets around the top and the bottom)

Try any expression in our order of operations calculator, which shows one step at a time.

• $-3^2 = -9$: the power applies to 3, then the negative.
• $(-3)^2 = 9$: the brackets make $-3$ the base.

Calculators follow this convention, which is why typing $-3^2$ gives $-9$. See negative numbers.

• Working strictly left to right and ignoring the order: $3 + 4 \times 2 \neq 14$.
• Doing all multiplication before any division (or the reverse).
• Forgetting that a fraction bar groups the top and the bottom.
• Treating "of" in BODMAS as a separate step: it means multiplication ("half of 10").

1. $6 + 18 \div 3$
2. $(6 + 18) \div 3$
3. $2 \times 3^2 + 4$
4. $40 \div 5 \times 2$

Answers: 12, 8, 22, 16. For more, see the order of operations topic guide.

The same rule is built into calculators, spreadsheets and programming languages. In a spreadsheet, =A1+B1*2 doubles B1 before adding A1; in Python, 2 + 3 * 4 gives 14. When you write formulas for other people, add brackets even when they're not strictly needed, such as =A1+(B1*2), so nobody has to remember the rule to read them.