Abeka 9th Grade Algebra 1 – Study Guide Chapter 2 Vocabulary Flashcards

Vocabulary flashcards covering signed numbers, absolute value, order of operations, simplifying expressions, translating word problems, problem-solving with charts, and related properties.

Signed Numbers

Numbers with a plus or minus sign used in addition, subtraction, multiplication, and division; rules determine the resulting sign.

Addition with Same Sign

If two numbers have the same sign, add their absolute values and keep that sign.

Addition with Different Signs

If two numbers have different signs, subtract the smaller absolute value from the larger and keep the sign of the larger magnitude.

Subtraction as Addition of Opposite

Subtracting a number is the same as adding its opposite.

Multiplication/Division Sign Rule

The product or quotient of two numbers with the same sign is positive; with different signs is negative.

Absolute Value

The nonnegative distance of a number from zero; |a| ≥ 0.

Absolute Value Examples

Examples: |−12| = 12; |7| = 7.

Simplify Inside Absolute Value

Inside the absolute value, simplify the expression first, then apply the absolute value.

Order of Operations (PEMDAS)

Parentheses, Exponents, Multiplication/Division from left to right, Addition/Subtraction from left to right.

Distributive Property

a(b + c) = ab + ac; example: −4(x − 6) = −4x + 24.

Combine Like Terms

Combine terms with the same variable factors by adding coefficients.

Evaluating Expressions

Substitute values for variables, then simplify.

Translating Word Problems into Algebra

Convert English statements into algebraic equations.

Example Translations

Twice a number increased by 7 is 19 → 2x + 7 = 19; The quotient of a number and 4 is 3 less than 10 → x/4 = 10 − 3.

Problem-Solving with Charts

Use charts to organize information before writing equations.