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Algebraic Expressions Worksheet

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Algebraic Expressions Worksheet

Identify parts of expressions, translate between words and algebra, and simplify. Show your work where space is provided.

Reading Algebraic Expressions

Look closely at how expressions are built from terms, variables, coefficients, constants, and operations.

1.For the expression 7m − 2n + 11, list its variables, coefficients, constant, and operation symbols.

2.In the expression 9p − 5q + 14, which number is the coefficient of p?

p
9
−5
14

3.Write each term in the expression 6r + 4s − 13 − 2r.

4.How many terms are in the expression 3x² − 8x + 5y + 12?

5.Match each algebra term to its description.

−6a
a
15
4b
+
b

variable
term
operation symbol
variable
constant
coefficient

Writing and Interpreting Expressions

Use a variable to stand for the unknown number or amount in each situation.

6.Write an expression for eight more than three times a number x.

7.Write an expression for the product of 5 and a number n, then decreased by 9.

8.Write an expression for four times the sum of a number k and 6.

9.Describe the expression 8w − 12 in words.

10.A museum ticket costs $14, and a group reservation has a one-time $5 fee. Write an expression for the cost of t tickets plus the fee.

11.Andre starts with $48 and spends $6 each week. Write an expression for the amount of money left after w weeks.

Simplifying Expressions

Combine like terms and use the distributive property. Keep unlike variables in separate terms.

12.Simplify: 4x + 9x − 5x.

13.Simplify: 7y + 6 − 3y + 10.

14.Simplify: 5a + 2b − 3a + 7b.

15.Use the distributive property to simplify 4(3x + 2).

16.Simplify completely: 3(2n − 5) + 5n + 4.

17.A craft kit costs $9, plus $3 for each extra item added. Write an expression for the cost of one kit with e extra items, then simplify the cost of 4 identical kits.