Algebraic Expressions

Unit Review Sheet

Facts and Definitions

Lesson 1: Introduction to Algebra

• Algebra is a branch of mathematics that deals with symbols (including numbers, variables, and operators) and the rules for working with those symbols.
• A constant is a number with a value that doesn't change.
• A variable is a value that is currently unknown or that can change. It is often represented by a letter (like x, y, or n).
• An algebraic expression is a mathematical phrase made up of variables, constants, and mathematical operations (like addition, subtraction, multiplication, and division).
• An equation is a number sentence that includes an equal sign (=).
• In an exponential expression, the base shows the value that is multiplied and the exponent shows the number of times the base is multiplied. Example: 3⁴ is the same as 3 × 3 × 3 × 3, which equals 81.

Lesson 2: Parts of an Expression

• Coefficient: a number attached to a variable by multiplication. For example, in the expression 7x, 7 is the coefficient. A variable printed without a shown number has a coefficient of 1.
• Term: a constant, variable, or combination of constants and variables. In an expression, different terms are separated by addition or subtraction symbols.
• Expressions are categorized by the number of terms they contain.
• Like terms: terms whose variables (including the variables' exponents) are exactly the same. Example: 7x² and 18x² are like terms because they both have x² as the variable component.
• Unlike terms: terms that have different variables (or the same variable with different exponents). Example: 7x and 18x² are unlike terms because x and x² have the same variable but different exponents.

Lesson 3: Working With Expressions

• The first step in translating a word problem into an algebra expression is to identify which value is unknown. This value is represented by a variable.
• To evaluate an expression means to find the value of the expression when a number value is substituted for the variable in the expression.

Lesson 4: Positive and Negative Numbers

• The opposite of the opposite of a number is the number itself. For example, the opposite of 4 is −4. The opposite of −4 is 4. So the opposite of the opposite of 4 is 4.
• Subtraction is the same as adding the opposite of the number that follows the subtraction sign. For example, 7 − 3 is the same as 7 + −3.
• To add a positive number to another positive number, add the numbers and keep the positive sign.
• To add a negative number to another negative number, add the numbers and keep the negative sign.
• To add a positive and negative number, subtract the numbers and use the sign of the number that is farther from zero.

Lesson 5: Equivalent Expressions

• Equivalent expressions are expressions that have the same value, even though they look different in form.
• To simplify an expression means to write it in the simplest possible form. The simplified expression is usually the easiest form to use for evaluating and solving.
• The commutative property says that the order of the numbers or variables doesn't matter in addition or multiplication.
• The associative property states that when adding or multiplying more than two numbers or variables, the order in which the numbers or variables are grouped doesn't matter.

Lesson 6: The Distributive Property

• The distributive property of multiplication states that multiplying the sum of two numbers or variables by a factor is the same as multiplying both numbers or variables by the factor and then adding the products.
• Expressions are equivalent if a real number value substituted for the variable(s) produces the same answer when the expressions are evaluated.

Lesson 7: Unit 4 Test

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Final Project: Algebra Think-Tac-Toe

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