Order of operations drills

Evaluate numeric expressions with PEMDAS incl. grouping, exponents, roots, and absolute value.

Free, timed SHSAT practice sets on order of operations— every question includes a full worked explanation, and there's no account required.

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How to solve order of operations problems

Use PEMDAS for the order of the steps:

  1. Parentheses and other grouping (brackets, absolute value bars, a fraction bar).
  2. Exponents and roots.
  3. Multiplication and Division, together, from left to right.
  4. Addition and Subtraction, together, from left to right.

Example: \(5 + 3^2 \times 2\). Exponent first: \(3^2 = 9\). Then multiply: \(9 \times 2 = 18\). Then add: \(5 + 18 = 23\).

Multiplication does not always come before division, and addition does not always come before subtraction. Each pair has the same rank, so go left to right: \(12 \div 3 \times 2 = 4 \times 2 = 8\), not 2.

Common traps: working straight left to right (\(2 + 3 \times 4\) is 14, not 20), and losing a minus sign. In \(9 - 9 \times 3 + 6\), the product is 27, so the answer is \(9 - 27 + 6 = -12\).

Worked examples

Example 1.
What is the value of \(8 + 9^2 \times 2\)?
Show answer and explanation
Answer:
D

Follow the order of operations: \(9^2 = 81\), then \(8 + 81 \times 2 = 170\). Adding before squaring gives \(578\). Adding before multiplying gives \(178\). Multiplying before squaring gives \(332\).

Example 2.
What is the value of \(11 - 11 \times 4 + 8\)?
Show answer and explanation
Answer:
C

Follow the order of operations: \(11 \times 4 = 44\), then \(11 - 44 + 8 = -25\). Working left to right (subtracting before multiplying) gives \(8\). Subtracting 8 too (as if the minus sign applied to everything after it) gives \(-41\). Adding before multiplying gives \(-121\).

Example 3.
What is the value of \(4 + 3 \times 7 - 5\)?
Show answer and explanation
Answer:
B

Follow the order of operations: \(3 \times 7 = 21\), then \(4 + 21 - 5 = 20\). Working left to right (adding before multiplying) gives \(44\). Subtracting before multiplying gives \(10\). Doing the addition and the subtraction before the multiplication gives \(14\).