How many practice problems are on this page?

This page has over 15 practice problems organized by difficulty (easy, medium, hard), plus 5 worked examples with full step-by-step solutions.

What is the best way to practice order of operations?

Work through problems in order from easy to hard. Write out every step rather than trying to do it in your head. Check your answers after each problem, and review the worked examples for any you got wrong.

Why do I keep getting the wrong answer for order of operations?

The most common reasons are: multiplying before dividing regardless of position (always go left to right), forgetting to apply PEMDAS inside parentheses, or skipping the exponent step.

How do I check my order of operations answer?

Use a calculator or work the problem a second time. Write each step on a separate line so you can trace exactly where an error occurred.

Order of Operations Practice Problems with Answers

Grade: 6-7 | Topic: Arithmetic

What You Will Learn

This page gives you focused practice on order of operations (PEMDAS/BODMAS). You will work through problems at three difficulty levels, review full step-by-step solutions, and strengthen the skills that students most commonly struggle with: the left-to-right rule, nested parentheses, and expressions with exponents.

Theory

Quick Review of PEMDAS

Before jumping into practice, here is the priority order:

$\text{Parentheses} \;\rightarrow\; \text{Exponents} \;\rightarrow\; \text{Multiplication / Division (left to right)} \;\rightarrow\; \text{Addition / Subtraction (left to right)}$

Remember:

Multiplication and Division have equal priority — go left to right
Addition and Subtraction have equal priority — go left to right
PEMDAS rules apply inside parentheses too
Work nested parentheses from the innermost group outward

Tips for Avoiding Mistakes

Write every step on a new line — do not try to do everything in your head.
Underline the operation you are about to perform next.
Rewrite the full expression after each step, replacing only the part you just calculated.
Double-check by working through the problem a second time.

Worked Examples

Example 1: Basic Expression (Easy)

Problem: Evaluate $5 + 8 \times 3$

Step 1 — Multiplication (Level 3):

$8 \times 3 = 24$

Step 2 — Addition (Level 4):

$5 + 24 = 29$

Answer: $\boxed{29}$

Example 2: Parentheses First (Easy)

Problem: Evaluate $(12 - 4) \times 3 + 1$

Step 1 — Parentheses:

$12 - 4 = 8$

Step 2 — Multiplication:

$8 \times 3 = 24$

Step 3 — Addition:

$24 + 1 = 25$

Answer: $\boxed{25}$

Example 3: Exponents and Mixed Operations (Medium)

Problem: Evaluate $4^2 - 3 \times 2 + 10 \div 5$

Step 1 — Exponent:

$4^2 = 16$

Expression becomes: $16 - 3 \times 2 + 10 \div 5$ .

Step 2 — Multiplication and division left to right:

$3 \times 2 = 6$

$10 \div 5 = 2$

Expression becomes: $16 - 6 + 2$ .

Step 3 — Addition and subtraction left to right:

$16 - 6 = 10$

$10 + 2 = 12$

Answer: $\boxed{12}$

Example 4: Nested Parentheses (Medium)

Problem: Evaluate $3 \times [2 + (6 - 1)]$

Step 1 — Innermost parentheses:

$6 - 1 = 5$

Expression becomes: $3 \times [2 + 5]$ .

Step 2 — Brackets:

$2 + 5 = 7$

Expression becomes: $3 \times 7$ .

Step 3 — Multiplication:

$3 \times 7 = 21$

Answer: $\boxed{21}$

Example 5: Everything Combined (Challenging)

Problem: Evaluate $\frac{(3 + 5)^2}{4} - 2 \times 3 + 1$

Step 1 — Parentheses:

$3 + 5 = 8$

Step 2 — Exponent:

$8^2 = 64$

Step 3 — Fraction bar (grouping):

$\frac{64}{4} = 16$

Expression becomes: $16 - 2 \times 3 + 1$ .

Step 4 — Multiplication:

$2 \times 3 = 6$

Expression becomes: $16 - 6 + 1$ .

Step 5 — Subtraction and addition left to right:

$16 - 6 = 10$

$10 + 1 = 11$

Answer: $\boxed{11}$

Common Mistakes

Mistake 1: Going left to right without checking for multiplication/division first

Expression: $2 + 6 \times 3$

❌ Left to right: $2 + 6 = 8$ , then $8 \times 3 = 24$ .

✅ PEMDAS: $6 \times 3 = 18$ , then $2 + 18 = 20$ .

Why this matters: Left to right only determines the order within the same priority level. Multiplication (Level 3) always comes before addition (Level 4).

Mistake 2: Doing exponents left to right instead of before multiplication

Expression: $2 \times 3^2$

❌ $2 \times 3 = 6$ , then $6^2 = 36$ .

✅ $3^2 = 9$ , then $2 \times 9 = 18$ .

Why this matters: Exponents (Level 2) have higher priority than multiplication (Level 3). Evaluate the exponent first.

Mistake 3: Forgetting to rewrite the expression after each step

Expression: $5 + 2 \times 3 - 4 \div 2$

❌ Trying to jump to the final answer without showing intermediate steps often leads to skipping operations or calculating them in the wrong order.

✅ Step by step:

$2 \times 3 = 6$ and $4 \div 2 = 2$ (Level 3)
Rewrite: $5 + 6 - 2$
Left to right: $5 + 6 = 11$ , then $11 - 2 = 9$

Why this matters: Rewriting forces you to keep track of every operation. This is the single best habit for avoiding errors.

Practice Problems

Level 1: Easy

$3 + 5 \times 2$
$10 - 4 + 6$
$(7 + 3) \times 2$
$18 \div 3 + 4$
$9 - 2 \times 3$

Click to see Level 1 answers

$3 + 10 = \mathbf{13}$
$6 + 6 = \mathbf{12}$ — left to right
$10 \times 2 = \mathbf{20}$ — parentheses first
$6 + 4 = \mathbf{10}$ — divide first
$9 - 6 = \mathbf{3}$ — multiply first

Level 2: Medium

$2^3 + 4 \times 5$
$36 \div 6 \times 3 - 2$
$(8 - 3)^2 + 7$
$4 \times (2 + 3) - 6 \div 2$
$50 - 3 \times [2 + (8 \div 4)]$

Click to see Level 2 answers

$8 + 20 = \mathbf{28}$ — exponent, then multiply, then add.
$6 \times 3 - 2 = 18 - 2 = \mathbf{16}$ — divide and multiply left to right, then subtract.
$5^2 + 7 = 25 + 7 = \mathbf{32}$ — parentheses, exponent, then add.
$4 \times 5 - 3 = 20 - 3 = \mathbf{17}$ — parentheses, then multiply and divide (left to right), then subtract.
Inner: $8 \div 4 = 2$ . Brackets: $2 + 2 = 4$ . Multiply: $3 \times 4 = 12$ . Subtract: $50 - 12 = \mathbf{38}$ .

Level 3: Hard

$2 + 3 \times (5^2 - 15) \div 2$
$[4 + 2 \times (3^2 - 1)] \div 5$
$\frac{6 + 2 \times 7}{4} + 3^2$
$10 - 2^3 + 4 \times 3 \div (6 - 4)$
$\frac{(5 - 2)^3 + 1}{7} \times 2 - 3$

Click to see Level 3 answers

Parentheses: $25 - 15 = 10$ . Then $3 \times 10 = 30$ . Then $30 \div 2 = 15$ . Finally $2 + 15 = \mathbf{17}$ .
Inner: $3^2 - 1 = 8$ . Then $2 \times 8 = 16$ . Brackets: $4 + 16 = 20$ . Then $20 \div 5 = \mathbf{4}$ .
Numerator: $2 \times 7 = 14$ , then $6 + 14 = 20$ . Fraction: $20 \div 4 = 5$ . Exponent: $3^2 = 9$ . Sum: $5 + 9 = \mathbf{14}$ .
Parentheses: $6 - 4 = 2$ . Exponent: $2^3 = 8$ . Multiply/divide: $4 \times 3 = 12$ , $12 \div 2 = 6$ . Left to right: $10 - 8 + 6 = \mathbf{8}$ .
Parentheses: $(5-2)^3 = 27$ . Numerator: $27 + 1 = 28$ . Fraction: $28 \div 7 = 4$ . Multiply: $4 \times 2 = 8$ . Subtract: $8 - 3 = \mathbf{5}$ .

Summary

Follow PEMDAS every time: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
Write every step on a separate line and rewrite the full expression after each calculation.
The most common errors come from ignoring the left-to-right rule, skipping the exponent step, or forgetting PEMDAS inside parentheses.
Practice at increasing difficulty levels — once you can handle Level 3 problems, you are ready for any test.

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What You Will Learn​

Theory​

Quick Review of PEMDAS​

Tips for Avoiding Mistakes​

Worked Examples​

Example 1: Basic Expression (Easy)​

Example 2: Parentheses First (Easy)​

Example 3: Exponents and Mixed Operations (Medium)​

Example 4: Nested Parentheses (Medium)​

Example 5: Everything Combined (Challenging)​

Common Mistakes​

Practice Problems​

Level 1: Easy​

Level 2: Medium​

Level 3: Hard​

Summary​

Related Topics​