Evaluate 6 + 3 × 4.
- Multiply before adding: 3 × 4 = 12.
- Add 6 + 12.
Answer: 18
Numerical Expressions Worksheets
Evaluate numerical expressions using grouping symbols and the order of operations. Show each intermediate step.
Learn the skill
Writing and evaluating numerical expressions
A numerical expression combines numbers and operations without an equals sign. To evaluate it, calculate its value. Grouping symbols show which calculation belongs together, especially when translating a sentence into mathematics.
A method you can use
- Identify the action described by each phrase: sum, difference, product, or quotient.
- Use parentheses when a whole sum or difference is an input to another operation.
- Evaluate grouping first, then powers, multiplication/division left to right, and addition/subtraction left to right.
Worked examples
Write and evaluate “three times the sum of six and four.”
- The sum is (6 + 4). The whole sum is multiplied by 3.
- Write 3 × (6 + 4), then calculate 3 × 10.
Answer: 30
Evaluate 24 ÷ 3 × 2 − 5.
- Division and multiplication have equal priority: 24 ÷ 3 = 8, then 8 × 2 = 16.
- Subtract 5 from 16.
Answer: 11
Find the mistake: treating multiplication as always first
A student evaluates 18 ÷ 3 × 2 as 18 ÷ 6 = 3. Which step changes the expression?
See the reasoning
The student grouped 3 × 2 even though no parentheses were given. Multiplication and division have equal precedence.
Evaluate left to right: 18 ÷ 3 = 6, then 6 × 2 = 12.
The student’s answer would be correct for a different expression, 18 ÷ (3 × 2). Parentheses change the grouping.
Try a transfer problem
Insert parentheses into 20 − 8 ÷ 4 so that the result is 3.
Check the solution
Subtract first: 20 − 8 = 12; then divide 12 by 4. Without the parentheses the value would be 18.
(20 − 8) ÷ 4 = 3
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. Evaluate 8 + 2 × 5.
Show answer and explanation
18
Multiply 2 × 5 = 10 before adding 8.
2. Write and evaluate “four times the difference of nine and two.”
Show answer and explanation
4 × (9 − 2) = 28
The difference is grouped first: 9 − 2 = 7; 4 × 7 = 28.
Before you begin
Add, subtract, multiply and divide whole numbers.
Choose your level
- Easy: Evaluate parentheses before multiplying or dividing.
- Medium: Combine parentheses, multiplication and subtraction.
- Hard: Evaluate nested grouping symbols and explain the order.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Evaluate: (7 + 5) × 4
2
Evaluate: (7 + 7) × 2
3
Evaluate: (10 + 3) × 2
4
Evaluate: (13 + 3) × 8
5
Evaluate: (6 + 7) × 11
6
Evaluate: (3 + 1) × 4
Answer Key
1. 482. 283. 264. 1285. 1436. 16