Math explorers

Variables and Algebraic Expressions

Grade 6Algebra

Learn with worked examples, then try the questions below.

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1Write expressions

A variable represents a number that can change or is not yet known. An expression has numbers, variables and operations, without an equals sign.

Worked exampleFive more than twice n → 2n + 5

2n means 2 × n. In 2n + 5, 2 is the coefficient and 5 is the constant.

2Evaluate expressions

Substitute the given value for each variable. Use the order of operations: grouping, powers, multiplication and division, then addition and subtraction.

Worked example3x + 2 when x = 4: 3 × 4 + 2 = 14

For 2(x + 5) when x = 6: first 6 + 5 = 11, then 2 × 11 = 22.

3Distributive property

Multiply the number outside the parentheses by every term inside. Keep subtraction signs with their terms.

Worked example3(x + 2) = 3x + 6

5(2y − 1) = 10y − 5. You can also factor: 6x + 9 = 3(2x + 3).

4Combine like terms

Like terms have the same variable part. Add or subtract their coefficients; keep constants together.

Worked example4x + 2x + 3 = 6x + 3

7a − 3a + 8 = 4a + 8. You cannot combine 3x and 2y into a single like term.

⭐ Try it yourself!

Question 1 of 5

Evaluate 4x + 3 when x = 5.

Need a hint?

Multiply 4 by 5, then add 3.