Order of Operations — Practice Problems and Worked Solutions

The formulas you need here

16 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Evaluate using the order of operations.

   $$3+2\cdot 4$$

   Answer: $11$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=11$$
2. 2.

   Evaluate using the order of operations.

   $$12÷3+2$$

   Answer: $6$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=6$$
3. 3.

   Evaluate using the order of operations.

   $$2(3+4)$$

   Answer: $14$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=14$$
4. 4.

   Evaluate using the order of operations.

   $$18-2^2\cdot 3$$

   Answer: $6$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=6$$
5. 5.

   Evaluate using the order of operations.

   $$(8-3{)}^2-4$$

   Answer: $21$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=21$$
6. 6.

   Evaluate using the order of operations.

   $$24÷(2\cdot 3)+5$$

   Answer: $9$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=9$$
7. 7.

   Evaluate using the order of operations.

   $$5+3\cdot 2$$

   Answer: $11$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=11$$
8. 8.

   Evaluate using the order of operations.

   $$20÷4-1$$

   Answer: $4$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=4$$
9. 9.

   Evaluate using the order of operations.

   $$3(2+5)$$

   Answer: $21$

   Step-by-step solution

   1. $$\text{Evaluate parentheses and powers first.}$$
   2. $$\text{Then multiply or divide from left to right.}$$
   3. $$=21$$
10. 10.

    Evaluate using the order of operations.

    $$30-3^2\cdot 2$$

    Answer: $12$

    Step-by-step solution

    1. $$\text{Evaluate parentheses and powers first.}$$
    2. $$\text{Then multiply or divide from left to right.}$$
    3. $$=12$$
11. 11.

    Evaluate using the order of operations.

    $$(6-2{)}^2+3$$

    Answer: $19$

    Step-by-step solution

    1. $$\text{Evaluate parentheses and powers first.}$$
    2. $$\text{Then multiply or divide from left to right.}$$
    3. $$=19$$
12. 12.

    Evaluate using the order of operations.

    $$36÷(3\cdot 2)-1$$

    Answer: $5$

    Step-by-step solution

    1. $$\text{Evaluate parentheses and powers first.}$$
    2. $$\text{Then multiply or divide from left to right.}$$
    3. $$=5$$
13. 13.

    Evaluate using the order of operations.

    $$4+6÷2$$

    Answer: $7$

    Step-by-step solution

    1. $$\text{Evaluate parentheses and powers first.}$$
    2. $$\text{Then multiply or divide from left to right.}$$
    3. $$=7$$
14. 14.

    Evaluate using the order of operations.

    $$2^3+4\cdot 3$$

    Answer: $20$

    Step-by-step solution

    1. $$\text{Evaluate parentheses and powers first.}$$
    2. $$\text{Then multiply or divide from left to right.}$$
    3. $$=20$$
15. 15.

    Evaluate using the order of operations.

    $$(9-4)\cdot 2+1$$

    Answer: $11$

    Step-by-step solution

    1. $$\text{Evaluate parentheses and powers first.}$$
    2. $$\text{Then multiply or divide from left to right.}$$
    3. $$=11$$
16. 16.

    Evaluate using the order of operations.

    $$50-2\cdot 5^2$$

    Answer: $0$

    Step-by-step solution

    1. $$\text{Evaluate parentheses and powers first.}$$
    2. $$\text{Then multiply or divide from left to right.}$$
    3. $$=0$$

More from Math Foundations

• Signed Numbers
• Fraction Sense
• Ratios and Percentages
• Exponents and Roots
• Algebraic Expressions
• Linear Equations
• Polynomial Basics
• Inequalities
• Coordinate Plane
• Reading Graphs
• Function Machines
• Substitution
• Factoring Basics