FLVS Algebra 1 Module 1 Foundations

Number Types

• Natural Numbers: Positive whole numbers excluding zero. Examples include 4, 7, 9.
• Whole Numbers: All positive whole numbers including zero. Examples are 0, 3, 6.
• Integers: Positive and negative whole numbers, including zero. Excludes fractions or decimals. Examples: -2, 0, 4.
• Rational Numbers: Numbers expressible as a ratio of two integers. Includes terminating or repeating decimals. Examples: 4/5, -14, 2.1, √4.
• Real Numbers: All non-imaginary numbers. Includes integers, rational numbers, and irrational numbers. Examples: -4, 1/3, √5, 3.2.

Integer Operations

• Addition/Subtraction (Same Sign): Sum the numbers and keep the sign. Examples: 4 + 5 = 9, -4 + -5 = -9.
• Addition/Subtraction (Different Signs): Find the absolute difference and keep the sign of the larger number. Examples: -6 + 2 = -4, 6 - 2 = 4.
• Double Signs: Change minus a negative to addition. Example: 3 - (-4) = 3 + 4 = 7.
• Opposite Signs: Simplify by substituting with the appropriate operation. Example: 3 + (-5) = 3 - 5 = -2.

Multiplication and Division

• Same Sign: The product or quotient is positive. Examples: (3)(4) = 12, -12/-3 = 4.
• Different Signs: The product or quotient is negative. Example: (-3)(4) = -12.

Algebraic Concepts

• PEMDAS: Order of operations stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
• Combining Like Terms: Only variables with the same base can be combined. Example: 2x + 3x = 5x.
• Coefficients: Numbers before variables indicating multiplication. Example: In 3x, 3 is the coefficient.
• Factors: Values that multiply together to yield a product. Examples include factors of 6: 1, 2, 3, 6.
• Exponents: Indicate repeated multiplication of a number. Example: (7^2 = 7 \times 7).
• Simplifying Expressions: Substitute values for variables and apply order of operations.

Units and Measurement

• Selecting Units: Choose units appropriate to the context (e.g., miles for long distances).
• Units in Formulas: Use compatible units in calculations. Example: (1 \text{ ft} \times 1 \text{ ft} = 1 \text{ ft}^2).
• Conversion Tables:
  • Distance: 1 inch = 2.54 cm, 1 mile = 1.609 km.
  • Weight: 1 pound = 16 ounces, 1 kg = 2.2 pounds.
  • Volume: 1 gallon = 3.785 liters, 1 cup = 8 fluid ounces.

Graphs and Data

• Graph Scales: Properly scale axes for clarity. The origin is (0, 0).
• Precision vs. Accuracy: Precision refers to data consistency; accuracy refers to how close data is to the true value.
• Rounding: Check significant figures for appropriate accuracy in answers.

Algebraic Properties

• Commutative Property: Order of numbers does not affect the result for addition/multiplication.
• Associative Property: Grouping of numbers does not affect the result for addition/multiplication.
• Distributive Property: Multiply a number by a sum or difference of terms. Example: (3(5 + 2) = 3 \cdot 5 + 3 \cdot 2).

Solving Equations

• Steps to Solve: Use distributive property, combine like terms, apply inverse operations to isolate the variable, and check solutions.
• Helpful Tips: Be cautious with signs when multiplying/dividing negatives, and take care of fractions with negatives.

Terms in Operations

• Addition Keywords: sum of, plus, total, more than, increased by.
• Subtraction Keywords: difference of, minus, less than, decreased by, subtracted from.
• Multiplication Keywords: product of, times, per.
• Division Keywords: quotient of, ratio of, half of, third of.

Translating Algebra

• Special Terms: Use keywords for clearly defining operations. "Twice the difference of n and 6" translates to 2(n - 6).
• Breaking Down Phrases: Highlight key words and translate gradually into algebraic expressions.

This quiz covers the foundational concepts of Algebra in Module 1 of FLVS Algebra 1. Learn about natural numbers, whole numbers, and integers through flashcards that define each term with examples. It’s an essential start to understanding algebraic principles.