Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 6th grade algebraic expressions? Then this Grade 6 lesson on Writing, Evaluating and Simplifying Algebraic Expressions explains each idea step by step, with worked examples.
Quick answer: An algebraic expression combines numbers, variables and operations, like 3n + 5. A variable is a letter standing for a number, and a coefficient is the number multiplying it. To evaluate, substitute a value for each variable and follow the order of operations. Equivalent expressions, made with the distributive property or by combining like terms, always have equal values.
Standards: 6.EE.A.2, 6.EE.A.3, 6.EE.A.4 · Level: Grade 6
What are variables, terms and coefficients?
- A variable is a letter that stands for a number that can change or is unknown.
- An algebraic expression combines numbers, variables and operation symbols, such as 5n + 3.
- A term is a part of an expression separated by + or −. A coefficient is the number multiplying a variable, and a constant is a term with no variable.
Writing a number next to a letter means multiplication, so 5n means 5 × n. The expression n ÷ 4 can also be written as a fraction with n on top and 4 on the bottom.
How do you write an expression from words?
| Words | Expression |
|---|---|
| 9 more than a number n | n + 9 |
| 9 less than a number n | n − 9 |
| twice a number n | 2n |
| a number n divided by 4 | n4 |
| 5 times the sum of n and 2 | 5(n + 2) |
Reversing “less than.” “9 less than n” is n − 9, not 9 − n.
How do you evaluate an expression or a formula?
- Replace every variable with its given value, using parentheses if helpful.
- Evaluate powers, then multiply and divide, then add and subtract, left to right.
The volume of a cube is V = s3 and its surface area is A = 6s2. For s = 4 inches: V = 4 × 4 × 4 = 64 cubic inches, and A = 6 × 16 = 96 square inches.
What are equivalent expressions?
Two expressions are equivalent when they have the same value for every number. The distributive property gives one pair: 4(x + 3) = 4x + 12. Combining like terms gives another: 3y + 4 + 2y + 1 = 5y + 5, because terms with the same variable part can be added.
Test your simplified answer: pick a number, such as 2, and check that both expressions give the same result.
- A term is a part of an expression separated by + or −.
- A coefficient multiplies a variable: in 7y, the coefficient is 7.
- To evaluate, substitute the value and use the order of operations.
- a(b + c) = ab + ac is the distributive property.
- Like terms have the same variable part and can be combined: 6x + 2x = 8x.
Writing, Evaluating and Simplifying Algebraic Expressions: frequently asked questions
What is the difference between an expression and an equation?
An expression, like 3n + 5, has no equal sign and cannot be solved. An equation, like 3n + 5 = 20, states that two expressions are equal and can be solved.
How do you tell the coefficient of a term?
The coefficient is the number multiplied by the variable. In 9m it is 9. If a variable has no number in front, such as x, its coefficient is 1.
What are like terms?
Like terms have exactly the same variable part, such as 4x and 7x. You can add or subtract their coefficients to combine them. The terms 4x and 7 are not like terms.
How can you check that two expressions are equivalent?
Substitute the same number into both and compare. If one value works but another does not, they are not equivalent. For a proof, use the distributive property or combine like terms.
Why does the formula V = s³ use an exponent?
A cube has three equal edge lengths, length, width and height, all equal to s. The volume multiplies them, s × s × s, which is written s³.
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