Basic Arithmetic and Number Systems

Basic Arithmetic Operations

• Addition: Combining two or more numbers to find their total. The sum is the result.
• Subtraction: Finding the difference between two numbers. The result is the difference.
• Multiplication: Repeated addition of a number. The product is the result.
• Division: Splitting a number into equal parts. The quotient is the result.

Number Systems

• Natural Numbers (counting numbers): 1, 2, 3, ...
• Whole Numbers: 0, 1, 2, 3, ... (includes zero)
• Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (includes negative numbers)
• Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. Examples include 1/2, 3/4, -2/5.
• Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers. Examples include √2, π.
• Real Numbers: The set of all rational and irrational numbers.

Properties of Numbers

• Commutative Property: Changing the order of numbers in addition or multiplication does not change the result.
• Associative Property: Changing the grouping of numbers in addition or multiplication does not change the result.
• Distributive Property: Multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
• Identity Property: The sum of any number and zero is the number itself. The product of any number and one is the number itself.
• Inverse Property: The sum of a number and its opposite is zero. The product of a number and its reciprocal is one (except for zero which has no reciprocal).

Fractions

• Fractions represent parts of a whole. A fraction has a numerator and a denominator.
• Equivalent Fractions: Fractions that represent the same portion of a whole.
• Simplifying Fractions: Reducing a fraction to its lowest terms by dividing the numerator and denominator by their greatest common factor (GCF).
• Adding and Subtracting Fractions: Requires finding a common denominator.
• Multiplying Fractions: Multiply the numerators and multiply the denominators.
• Dividing Fractions: Multiply the first fraction by the reciprocal of the second fraction.

Decimals

• Decimals represent parts of a whole using place value.
• Converting between decimals and fractions.
• Adding, Subtracting, Multiplying, and Dividing Decimals.

Exponents and Radicals

• Exponents represent repeated multiplication.
• Evaluating expressions involving exponents and radicals.

Algebra

• Variables represent unknown quantities.
• Equations express equality between two expressions.
• Solving equations involves isolating the variable.
• Inequalities compare two expressions using symbols like <, >, ≤, ≥.
• Linear equations: Equations that can be graphed as straight lines.
• Systems of equations: Two or more equations with the same variables.

Geometry

• Basic shapes (triangles, circles, squares, rectangles).
• Perimeter, area, and volume of common shapes.
• Angles and their properties.
• Lines and their properties.

Measurement

• Units of measurement (length, weight, volume, time, temperature).
• Converting between different units of measurement.

Data Analysis

• Collecting data and organizing it in tables or graphs.
• Measures of central tendency (mean, median, mode).
• Measures of variability (range, standard deviation).
• Interpreting data presented in graphs and tables.

Probability

• Likelihood of events occurring.
• Basic probability calculations.
• Probability distributions.

Statistics

• Collecting and analyzing numerical data.
• Descriptive statistics summarize data (mean, median, etc).
• Inferential statistics uses sample data to draw conclusions about a wider population.

Problem Solving

• Steps for solving math problems.
• Identifying unknowns, creating equations, solving equations, and verifying the results.

Special Topics

• Significant figures/rounding
• Pythagorean theorem
• Functions