Order of operations (PEMDAS) and the traps tests use

Order of operations questions are some of the easiest marks to lose on the EIAT, because the wrong answer is almost always one of the options. The rules are simple; the traps are in the details.

PEMDAS

Work through an expression in this order:

1. Parentheses — anything in brackets first.
2. Exponents — powers and roots.
3. Multiplication and Division — together, working left to right.
4. Addition and Subtraction — together, working left to right.

Trap 1: multiplication does not always come before division

PEMDAS lists M before D, which makes people think multiplication goes first. It does not. Multiplication and division have equal priority, so you do them in the order they appear, left to right.

8 ÷ 2 × 4: left to right, 8 ÷ 2 = 4, then 4 × 4 = 16. Doing the multiplication first gives 8 ÷ 8 = 1, which is wrong.

Trap 2: the same for addition and subtraction

10 − 4 + 3: left to right, 10 − 4 = 6, then 6 + 3 = 9. Adding first gives 10 − 7 = 3, which is wrong.

Trap 3: multiplication before addition

2 + 3 × 4 = 2 + 12 = 14, not 20. Only brackets change that: (2 + 3) × 4 = 20.

Trap 4: exponents and negatives

An exponent applies only to what it is directly attached to. −3² means −(3²) = −9, whereas (−3)² = 9.

Trap 5: a fraction bar groups things

A long fraction bar acts like brackets around the top and around the bottom. Work each out fully before dividing: (6 + 4) ÷ (3 − 1) = 10 ÷ 2 = 5.

A full worked example

18 − 6 ÷ 3 × 2 + 4²

1. Exponent: 4² = 16. Now 18 − 6 ÷ 3 × 2 + 16.
2. Division and multiplication, left to right: 6 ÷ 3 = 2, then 2 × 2 = 4. Now 18 − 4 + 16.
3. Subtraction and addition, left to right: 18 − 4 = 14, then 14 + 16 = 30.

How to avoid the traps on test day

• Rewrite the expression after each step, as in the example above. It is slower, and it catches nearly every mistake.
• When a line has both × and ÷ (or + and −), underline them and work left to right.
• Check your answer against the options exactly — and remember "No answer" is a real option on the EIAT.

Practice

The EIAT math practice includes order-of-operations questions where the most common wrong answer is always among the options.