Overview
This lecture reviewed foundational math concepts needed for algebra, including types of numbers, prime vs. composite, simplifying fractions, using calculators, number lines, and place value and rounding.
Types of Numbers
- Natural numbers are counting numbers starting from 1 (1, 2, 3, ...).
- Whole numbers include all natural numbers plus 0 (0, 1, 2, 3, ...).
- Integers include whole numbers and their negatives (..., -2, -1, 0, 1, 2, ...).
Prime and Composite Numbers
- A prime number has exactly two factors: 1 and itself.
- Examples of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
- A composite number has more than two factors (e.g., 4, 6, 8, 9, 10).
- The number 1 is neither prime nor composite.
Least Common Multiple (LCM)
- LCM is the smallest number that is a multiple of two or more numbers.
- To find the LCM, list the multiples of each number and identify the smallest common value.
Simplifying Fractions
- Simplify by dividing both numerator and denominator by their greatest common factor.
- Example: 2/6 simplifies to 1/3 because both are divisible by 2.
- The numerator is the top number; the denominator is the bottom number.
Calculator Use with Fractions
- Use parentheses to enter fractions in calculators.
- Use the math function to convert decimals to fractions.
- Multiply or add fractions directly and simplify as needed.
Division and Zero Rules
- Any number divided by zero is undefined.
- Zero divided by any number is zero.
Evaluating Algebraic Expressions
- Substitute the given value for the variable to evaluate expressions.
- Example: For x = 4, 5x = 5 × 4 = 20.
- When a number and variable are together (e.g., 5x), it means multiplication.
Plotting on a Number Line
- Positive numbers are to the right of zero; negatives to the left.
- Decimals and fractions can be located between whole numbers by converting to decimal form.
Place Value and Rounding
- Tenths place is one digit after the decimal; round up if the next digit is 5 or more.
- Hundredths place is two digits after the decimal.
- Thousandths place is three digits after the decimal.
Key Terms & Definitions
- Natural Numbers — Counting numbers starting from 1.
- Whole Numbers — All natural numbers plus zero.
- Integer — Whole numbers and their negatives.
- Prime Number — A number whose only factors are 1 and itself.
- Composite Number — A number greater than 1 that is not prime.
- LCM (Least Common Multiple) — The smallest multiple common to two or more numbers.
- Numerator — Top number of a fraction.
- Denominator — Bottom number of a fraction.
- Reciprocal — The result of swapping the numerator and denominator of a fraction.
- Undefined — Division by zero has no meaning in mathematics.
Action Items / Next Steps
- Review your notes and complete the lesson one homework.
- Watch the calculator basics video as assigned.
- Practice classifying numbers, finding LCMs, simplifying fractions, and evaluating expressions.