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Basic Arithmetic Operations

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

Number Systems

• Natural Numbers: Counting numbers (e.g., 1, 2, 3,...).
• Whole Numbers: Natural numbers and zero (e.g., 0, 1, 2, 3,...).
• Integers: Whole numbers and their negative counterparts (e.g.,..., -3, -2, -1, 0, 1, 2, 3,...).
• Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero. Examples include 1/2, -3/4, 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.

Fractions

• A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number).
• Equivalent fractions: Fractions that represent the same value.
• Simplifying fractions: Reducing a fraction to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD).
• Adding and subtracting fractions: Requires finding a common denominator.
• Multiplying fractions: Multiply the numerators and multiply the denominators.
• Dividing fractions: Invert the second fraction and multiply.

Decimals

• A decimal represents a fraction with a denominator of 10, 100, 1000, and so on.
• Converting fractions to decimals: Divide the numerator by the denominator.
• Converting decimals to fractions: Identify the place value of the last digit and write the decimal as a fraction.
• Adding and subtracting decimals: Line up the decimal points.
• Multiplying decimals: Multiply as if they are whole numbers, then place the decimal point in the product.
• Dividing decimals: Move the decimal point in the divisor and dividend to the right until the divisor is a whole number. Move the decimal point in the quotient accordingly.

Exponents and Powers

• Exponent: A number that indicates how many times a base number is multiplied by itself.
• Power: The result of raising a base number to an exponent.
• Base: The number that is raised to a power.
• Negative Exponents: A negative exponent indicates reciprocal.
• Laws of exponents: Rules that govern operations with exponents.

Factors and Multiples

• Factor: A number that divides another number exactly (without a remainder).
• Multiple: A number that is a product of a given number and an integer.
• Prime Numbers: Numbers greater than 1 that have only two factors: 1 and itself.
• Composite Numbers: Numbers greater than 1 that have more than two factors.
• Greatest Common Factor (GCF): The largest factor that divides two or more numbers.
• Least Common Multiple (LCM): The smallest multiple that two or more numbers share.

Order of Operations (PEMDAS/BODMAS)

• Parentheses/Brackets
• Exponents/Orders
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Percentages

• Percentage: A ratio that compares a number to 100.
• Converting fractions to percentages: Multiply the fraction by 100%.
• Converting decimals to percentages: Multiply the decimal by 100%.
• Converting percentages to fractions or decimals: Divide the percentage by 100.
• Applications of percentages: Discount, sales tax, interest, etc.

Ratio and Proportion

• Ratio: A comparison of two or more quantities.
• Proportion: An equation that states that two ratios are equal.
• Solving proportions: Use cross-multiplication to find unknown values.

Geometry (Basic Concepts)

• Points, lines, planes: Fundamental geometric objects.
• Angles: Formed by two rays with a common endpoint.
• Types of angles: Acute, obtuse, right, straight, reflex.
• Polygons: Two-dimensional shapes with straight sides.
• Area and Perimeter: Measures describing the size and boundary of shapes.