Pre-Algebra is a branch of mathematics that prepares students for the study of algebra. It includes various fundamental concepts such as working with integers, understanding factors and multiples, prime factorization, solving basic equations and inequalities, and graphing on the coordinate plane. These topics are essential for developing the skills needed to tackle algebraic expressions, equations, and functions.
Integers are whole numbers that can be positive, negative, or zero. Understanding how to work with integers is a foundational skill in Pre-Algebra. Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always a non-negative number.
For a detailed exploration of this topic, visit our section on Integers & Absolute Values.
Example: Calculating Absolute Values
Find the absolute value of -7. Step 1: Ignore the negative sign and find the distance from 0. Answer: The absolute value of -7 is 7.
Factors are numbers that divide evenly into another number, while multiples are the result of multiplying a number by an integer. Understanding factors and multiples is critical for working with fractions, simplifying expressions, and solving problems involving divisibility.
Explore more about this topic in our Factors & Multiples section.
Example: Finding Factors
Find all factors of 18. Step 1: Start with 1 and 18 (since 1×18=18). Step 2: Check 2 (2×9=18) and 3 (3×6=18). Answer: The factors of 18 are 1, 2, 3, 6, 9, 18.
Prime factorization involves breaking down a number into its prime factors. Prime numbers are the building blocks of all numbers, and understanding how to factorize numbers is essential for solving various mathematical problems, including simplifying fractions and finding the greatest common divisors (GCD).
Learn more by visiting our Prime Factorization page.
Example: Prime Factorization
Find the prime factorization of 60. Step 1: Divide 60 by the smallest prime number 2 (60 ÷ 2 = 30). Step 2: Divide 30 by 2 again (30 ÷ 2 = 15). Step 3: 15 is divisible by 3 (15 ÷ 3 = 5). 5 is prime. Answer: The prime factorization of 60 is 2² × 3 × 5.
Equations and inequalities are fundamental concepts in algebra. An equation states that two expressions are equal, while an inequality indicates that one expression is greater or less than another. Learning how to solve these is crucial for success in algebra and beyond.
For an in-depth look, check out our section on Basic Equations & Inequalities.
Example: Solving a Basic Equation
Solve the equation 2x + 3 = 11. Step 1: Subtract 3 from both sides (2x = 8). Step 2: Divide both sides by 2 (x = 4). Answer: The solution is x = 4.
The coordinate plane is a two-dimensional surface on which points are plotted based on their x (horizontal) and y (vertical) coordinates. Graphing equations on the coordinate plane is a key skill in algebra and helps in visualizing relationships between variables.
Dive deeper into this topic by visiting our Coordinate Plane & Graphing page.
Example: Plotting Points on the Coordinate Plane
Plot the point (3, 4) on the coordinate plane. Step 1: Start at the origin (0, 0). Step 2: Move 3 units to the right (positive x direction). Step 3: Move 4 units up (positive y direction). Answer: The point (3, 4) is plotted.
