Order of Operations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Order of Operations.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The agreed-upon sequence for evaluating expressions: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Without rules, 2+3×42 + 3 \times 4 could mean 20 or 14. We agree to multiply first: 14.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A fixed sequence — parentheses, then exponents, then times/divide, then add/subtract — so everyone reads an expression the same way.

Common stuck point: The procedure for order of operations is the easy part; the trap is doing addition before multiplication because it comes first left to right. Asking "Does this expression have more than one operation that needs an agreed order?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does this expression have more than one operation that needs an agreed order?

Worked Examples

Example 1

easy
Evaluate 3+4×23 + 4 \times 2.

Answer

1111

First step

1
Identify the operations present: multiplication and addition.

Full solution

  1. 2
    Apply PEMDAS: multiplication before addition. Compute 4×2=84 \times 2 = 8.
  2. 3
    Now add: 3+8=113 + 8 = 11.
The order of operations (PEMDAS/BODMAS) tells us to perform multiplication before addition, even when addition appears first in the expression.

Example 2

medium
Evaluate 2×(3+5)2−10÷22 \times (3 + 5)^2 - 10 \div 2.

Example 3

medium
Evaluate 23+4×(5−2)2−6÷32^3 + 4 \times (5 - 2)^2 - 6 \div 3 step by step.

Example 4

medium
Evaluate [(2+3)×4−6]÷7[(2+3) \times 4 - 6] \div 7.

Example 5

hard
Insert parentheses into 3+2×5−13 + 2 \times 5 - 1 to make the value equal 2020.

Example 6

challenge
Evaluate (2+3)2−4⋅232−2⋅3+1\frac{(2 + 3)^2 - 4 \cdot 2}{3^2 - 2 \cdot 3 + 1}.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
Evaluate 18−3×(4+1)+2318 - 3 \times (4 + 1) + 2^3.

Example 2

hard
Evaluate 5+32×2−(12÷4+1)5 + 3^2 \times 2 - (12 \div 4 + 1).

Example 3

easy
Compute 3+4×23 + 4 \times 2.

Example 4

easy
Compute (3+4)×2(3 + 4) \times 2.

Example 5

easy
Compute 8−2×38 - 2 \times 3.

Example 6

easy
Compute 20÷4+320 \div 4 + 3.

Example 7

easy
Compute 6÷2+3×26 \div 2 + 3 \times 2.

Example 8

easy
Compute 52−15^2 - 1.

Example 9

easy
Compute 2×322 \times 3^2.

Example 10

easy
Compute −32-3^2.

Example 11

medium
Compute (2+3)2−4×5(2 + 3)^2 - 4 \times 5.

Example 12

medium
Compute 48÷6÷248 \div 6 \div 2.

Example 13

medium
Compute 4+2×(5−1)24 + 2 \times (5 - 1)^2.

Example 14

medium
Compute 8+42×3\frac{8 + 4}{2 \times 3}.

Example 15

medium
Compute 20−32+420 - 3^2 + 4.

Example 16

medium
Compute 2×(3+4×2)2 \times (3 + 4 \times 2).

Example 17

medium
Compute 24÷2(3+1)24 \div 2(3 + 1).

Example 18

medium
Compute 10−[3+2×(4−1)]10 - [3 + 2 \times (4 - 1)].

Example 19

medium
Compute 16+3×2\sqrt{16} + 3 \times 2.

Example 20

challenge
Insert parentheses to make 5+3×2−1=155 + 3 \times 2 - 1 = 15 true.

Example 21

challenge
Compute 32+4×5(7−5)2\frac{3^2 + 4 \times 5}{(7 - 5)^2}.

Example 22

challenge
Compute 2+22+222 + 2^{2 + 2^2}.

Example 23

easy
Compute 7+2×37 + 2 \times 3.

Example 24

easy
Compute (7+2)×3(7 + 2) \times 3.

Example 25

easy
Compute 10−6+310 - 6 + 3.

Example 26

easy
Compute 32+423^2 + 4^2.

Example 27

easy
Compute 12÷3×212 \div 3 \times 2.

Example 28

easy
Compute 9−4−29 - 4 - 2.

Example 29

medium
Compute 5+2×(32−4)5 + 2 \times (3^2 - 4).

Example 30

medium
Compute 12+3×46\frac{12 + 3 \times 4}{6}.

Example 31

medium
Compute 100−4×(3+2)2100 - 4 \times (3 + 2)^2.

Example 32

medium
Compute (8−2)23+1\frac{(8 - 2)^2}{3} + 1.

Example 33

medium
Compute 4×3+2×54 \times 3 + 2 \times 5.

Example 34

medium
Compute 9+16\sqrt{9 + 16}.

Example 35

medium
Compute 6+2×32−4÷26 + 2 \times 3^2 - 4 \div 2.

Example 36

hard
Compute 5×4−223+1\frac{5 \times 4 - 2^2}{3 + 1}.

Example 37

hard
Compute 2×32−(4+1)2+72 \times 3^2 - (4 + 1)^2 + 7.

Example 38

hard
Compute ((3+1)×2)2−5×3((3+1) \times 2)^2 - 5 \times 3.

Example 39

hard
Compute 3+2×16−53 + 2 \times \sqrt{16} - 5.

Example 40

challenge
Compute 2322^{3^2} (right-associative exponent).
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Background Knowledge

These ideas may be useful before you work through the harder examples.

additionsubtractionmultiplicationdivision