Practice Operation Hierarchy in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The layered relationship between arithmetic operations, where each is built from the previous: multiplication from addition, exponentiation from multiplication.

Multiplication is repeated addition. Exponents are repeated multiplication.

Showing a random 20 of 50 problems.

Example 1

easy
Evaluate 10−2×3+110 - 2 \times 3 + 1.

Example 2

hard
Evaluate 24−2×35\dfrac{2^4 - 2 \times 3}{5}.

Example 3

hard
Evaluate −32+(−3)2-3^2 + (-3)^2.

Example 4

challenge
Evaluate 2+3×(4−1)22 + 3 \times (4 - 1)^2.

Example 5

medium
Evaluate 6+2×5−4÷26 + 2 \times 5 - 4 \div 2.

Example 6

easy
Is 232^3 equal to 2×32 \times 3? (yes/no)

Example 7

medium
Evaluate 42−15\dfrac{4^2 - 1}{5}.

Example 8

hard
Evaluate 16+3×22−6÷3\sqrt{16} + 3 \times 2^2 - 6 \div 3.

Example 9

easy
In 8−6÷28 - 6 \div 2, which operation comes first?

Example 10

medium
Evaluate 2+3×422 + 3 \times 4^2.

Example 11

medium
Evaluate 2+32×(4−1)÷92 + 3^2 \times (4 - 1) \div 9.

Example 12

medium
Evaluate 48÷2÷448 \div 2 \div 4.

Example 13

easy
Evaluate 9−229 - 2^2.

Example 14

medium
Evaluate 36÷6+2×336 \div 6 + 2 \times 3.

Example 15

easy
Which operation is at the top of the hierarchy: addition, multiplication, or exponentiation?

Example 16

medium
Evaluate 23+222^3 + 2^2.

Example 17

easy
Evaluate 12÷4+312 \div 4 + 3.

Example 18

medium
Evaluate (2+3)×42(2 + 3) \times 4^2.

Example 19

easy
Rewrite 232^3 as repeated multiplication.

Example 20

medium
Evaluate 50−32×250 - 3^2 \times 2.
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