Order of Operations I Worksheets

Evaluate expressions with addition, subtraction, multiplication and parentheses. Answers can be negative. Grades 7–9.

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What these worksheets practise

The order of operations is the agreement that lets everyone get the same answer from the same expression: work inside parentheses first, then multiply, then add and subtract from left to right. Without it, 4+3×54 + 3 \times 5 could be read as 35 or 19; with it, the answer is always 19.

Order of Operations I uses only ++, −-, ×\times and parentheses. Each operation in a problem is chosen at random, so one expression may contain several multiplications and the next none at all. Answers can be negative, which makes these worksheets a good fluency check once integers are familiar. The Pre-Algebra order of operations worksheets, where every Easy and Medium problem has exactly one multiplication, are the gentler introduction; Order of Operations II adds exponents, division and brackets.

  • Easy — three numbers from 2 to 9 with one multiplication and no parentheses.
  • Medium — four numbers up to 12 with one pair of parentheses.
  • Hard — five numbers up to 15 with parentheses, often two groups.

Worked examples

Easy: 4+3×54 + 3 \times 5

Multiply before adding:

4+3×5=4+15=194 + 3 \times 5 = 4 + 15 = 19

Medium: 12−(3+5)×212 - (3 + 5) \times 2

Parentheses first, then multiplication, then subtraction:

12−(3+5)×2=12−8×2=12−16=−412 - (3 + 5) \times 2 = 12 - 8 \times 2 = 12 - 16 = -4

Hard: (6+9)×(14−11)−7(6 + 9) \times (14 - 11) - 7

Evaluate both groups, multiply, then subtract:

(6+9)×(14−11)−7=15×3−7=45−7=38(6 + 9) \times (14 - 11) - 7 = 15 \times 3 - 7 = 45 - 7 = 38

Check your answers

Rewrite the expression one step per line, doing exactly one operation each time. If a calculator is allowed, a scientific calculator follows the same order and gives −4-4 for the medium example.

Common mistakes

  • Working strictly left to right. 4+3×54 + 3 \times 5 is not 7×5=357 \times 5 = 35. Multiplication comes first.
  • Subtracting too early. In 12−8×212 - 8 \times 2, computing 12−8=412 - 8 = 4 first gives 8 instead of −4-4.
  • Adding before subtracting. Addition and subtraction have equal rank and go left to right: 10−4+3=910 - 4 + 3 = 9, not 10−7=310 - 7 = 3.
  • Dropping the negative sign. 12−16=−412 - 16 = -4. A negative result is a correct answer.

Sample problems

These problems come from the same generator as the worksheet above, three at each difficulty level. Press Generate for a fresh set.

Easy

  1. 6×2+8=6 \times 2 + 8 =
  2. 7×7−4=7 \times 7 - 4 =
  3. 4+8×5=4 + 8 \times 5 =

Medium

  1. 8×2+(11−8)=8 \times 2 + (11 - 8) =
  2. 6+(11+4)+12=6 + (11 + 4) + 12 =
  3. (9+9)+9×4=(9 + 9) + 9 \times 4 =

Hard

  1. (4×6)×(12−5)−2=(4 \times 6) \times (12 - 5) - 2 =
  2. (11−10)×(12−12)+3=(11 - 10) \times (12 - 12) + 3 =
  3. 2+(7+7−15)+10=2 + (7 + 7 - 15) + 10 =
Show answers
  1. 20
  2. 45
  3. 44
  4. 19
  5. 33
  6. 54
  7. 166
  8. 3
  9. 11

Tips for teachers and parents

  • Ask students to underline the operation they will do next before writing each line. It slows down the students who rush and shows where an error started.
  • "PEMDAS" is a useful memory aid as long as students know that M/D and A/S are pairs done left to right, not strict one-after-the-other steps.
  • Move on to Order of Operations II once students are accurate on Hard.

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