ARITHMETIC

Order of Operations Practice Problems

10 PEMDAS problems in 3 levels. Work each one on paper, then open the answer to check every step, or send it straight to the calculator.

• 10 problems
01

The Rules in 30 Seconds

  1. Parentheses (and brackets) first, innermost first.
  2. Exponents next.
  3. Multiplication and division, whichever comes first from left to right.
  4. Addition and subtraction, whichever comes first from left to right.

PEMDAS, BODMAS, BIDMAS and BEDMAS all describe this same order. Need a refresher? The Order of Operations Calculator page explains each rule with examples.

03

Level 2: Exponents and Equal Ranks

Exponents, plus the left-to-right rule for operations of equal rank.

  1. 18 ÷ 3 × 2
    Show answer
    1. ÷ and × are equal, so go left to right: 18 ÷ 3 = 6
    2. Then 6 × 2 = 12

    Answer: 12 · See every step in the calculator →

  2. 5 + 3^2 × 2
    Show answer
    1. Exponent first: 3² = 9
    2. Multiply: 9 × 2 = 18
    3. Add: 5 + 18 = 23

    Answer: 23 · See every step in the calculator →

  3. 40 − 5 × (3 + 4)
    Show answer
    1. Parentheses: 3 + 4 = 7
    2. Multiply: 5 × 7 = 35
    3. Subtract: 40 − 35 = 5

    Answer: 5 · See every step in the calculator →

  4. 9 − 6 + 2
    Show answer
    1. − and + are equal, so go left to right: 9 − 6 = 3
    2. Then 3 + 2 = 5

    Answer: 5 · See every step in the calculator →

04

Level 3: Putting It All Together

Nested brackets, exponents and every operation in one problem.

  1. 2 × (3 + 5)^2 ÷ 16
    Show answer
    1. Parentheses: 3 + 5 = 8
    2. Exponent: 8² = 64
    3. Left to right: 2 × 64 = 128
    4. 128 ÷ 16 = 8

    Answer: 8 · See every step in the calculator →

  2. 50 − [4 × (6 − 2)] + 3^2
    Show answer
    1. Innermost brackets: 6 − 2 = 4
    2. Outer brackets: 4 × 4 = 16
    3. Exponent: 3² = 9
    4. Left to right: 50 − 16 = 34, then 34 + 9 = 43

    Answer: 43 · See every step in the calculator →

  3. (12 − 4) ÷ 2 + 3 × (2 + 1)^2 − 10
    Show answer
    1. Parentheses: 12 − 4 = 8 and 2 + 1 = 3
    2. Exponent: 3² = 9
    3. Divide and multiply: 8 ÷ 2 = 4 and 3 × 9 = 27
    4. Left to right: 4 + 27 = 31, then 31 − 10 = 21

    Answer: 21 · See every step in the calculator →

05

Bonus: The Negative-Sign Trap

What is −2^2 + (−2)^2?

Show answer
  1. −2² means −(2²) = −4, because the exponent comes before the minus sign
  2. (−2)² = 4, because the brackets make the whole −2 the base
  3. −4 + 4 = 0

Answer: 0 · See every step in the calculator →