Math Basics: Numbers and Operations

Numbers and Operations

• Types of Numbers:
  • Natural Numbers: 1, 2, 3, ...
  • Whole Numbers: 0, 1, 2, 3, ...
  • Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
  • Rational Numbers: fractions, decimals, and percents
  • Irrational Numbers: non-repeating decimals, e.g. π, e
• Basic Operations:
  • Addition: combining two or more numbers to get a total or sum
  • Subtraction: finding the difference between two numbers
  • Multiplication: repeated addition of a number
  • Division: sharing a number into equal parts or groups
• Order of Operations:
  1. Parentheses (if present)
  2. Exponents (if present)
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)

Fractions and Decimals

• Fractions:
  • Numerator: the top number
  • Denominator: the bottom number
  • Equivalent Fractions: fractions with the same value, e.g. 1/2 = 2/4
  • Simplifying Fractions: reducing a fraction to its simplest form
• Decimals:
  • Converting Fractions to Decimals: dividing the numerator by the denominator
  • Rounding Decimals: approximating a decimal to a specific number of places
• Percentages:
  • Converting Decimals to Percentages: multiplying by 100
  • Finding a Percentage of a Number: multiplying the number by the percentage

Algebra and Geometry

• Variables and Expressions:
  • Variables: letters or symbols representing unknown values
  • Expressions: combinations of numbers, variables, and operations
  • Evaluating Expressions: substituting values for variables
• Basic Geometry:
  • Points: locations in space
  • Lines: sets of points extending infinitely
  • Angles: formed by two lines or rays
  • Shapes: basic geometric figures, e.g. triangles, quadrilaterals, circles

Ratios and Proportions

• Ratios:
  • Comparing two quantities, e.g. 2:3 or 2/3
  • Simplifying Ratios: reducing a ratio to its simplest form
• Proportions:
  • Equating two ratios, e.g. 2:3 = 4:6
  • Solving Proportions: finding the unknown value in a proportion

Numbers and Operations

• Natural Numbers are 1, 2, 3, and so on.
• Whole Numbers are 0, 1, 2, 3, and so on.
• Integers are ..., -3, -2, -1, 0, 1, 2, 3, and so on.
• Rational Numbers are fractions, decimals, and percents.
• Irrational Numbers are non-repeating decimals, such as π and e.
• Addition combines two or more numbers to get a total or sum.
• Subtraction finds the difference between two numbers.
• Multiplication is repeated addition of a number.
• Division shares a number into equal parts or groups.

Order of Operations

• Evaluate expressions inside parentheses first.
• Evaluate expressions with exponents next.
• Evaluate expressions with multiplication and division from left to right.
• Finally, evaluate expressions with addition and subtraction from left to right.

Fractions and Decimals

• The numerator is the top number in a fraction.
• The denominator is the bottom number in a fraction.
• Equivalent Fractions are fractions with the same value, such as 1/2 = 2/4.
• Simplifying Fractions reduces a fraction to its simplest form.
• Converting fractions to decimals involves dividing the numerator by the denominator.
• Rounding decimals approximates a decimal to a specific number of places.

Percentages

• Converting decimals to percentages involves multiplying by 100.
• Finding a percentage of a number involves multiplying the number by the percentage.

Algebra and Geometry

• Variables are letters or symbols representing unknown values.
• Expressions are combinations of numbers, variables, and operations.
• Evaluating expressions involves substituting values for variables.
• Points are locations in space.
• Lines are sets of points extending infinitely.
• Angles are formed by two lines or rays.
• Shapes are basic geometric figures, such as triangles, quadrilaterals, and circles.

Ratios and Proportions

• Ratios compare two quantities, such as 2:3 or 2/3.
• Simplifying ratios reduces a ratio to its simplest form.
• Proportions equate two ratios, such as 2:3 = 4:6.
• Solving proportions involves finding the unknown value in a proportion.