Algebra 1, Part 2

To simplify a fraction means to express it in its simplest or most reduced form. It involves reducing the numerator and denominator to their smallest possible values by dividing both of them by their greatest common divisor (GCD).

Diamond Problems are an excellent way of practicing addition, subtraction, multiplication, and division of positive and negative integers, decimals and fractions. They have the added benefit of preparing students for factoring binomials in algebra. 

Evaluating expressions refers to the process of finding the numerical value of a mathematical expression by substituting given values for the variables and performing the necessary operations. An expression is a combination of numbers, variables, and mathematical symbols, such as addition, subtraction, multiplication, division, and exponentiation.

Solving multi-step equations involves a series of steps to determine the value of the variable(s) in an equation that contains multiple operations. The goal is to isolate the variable on one side of the equation and find its numerical value.

In this module we take a look at how to graph linear equations given point-slope form or slope intercept form.

Multiplying polynomials is an important skill in algebra that helps us combine and expand expressions with variables and coefficients. It allows us to solve equations, simplify expressions, and explore mathematical relationships. One useful method for multiplying polynomials is using rectangles.

This method breaks down the multiplication process into simpler steps using rectangles. It helps us understand the concepts visually before using symbols and formulas.

Sometimes we are given two linear equations, and we are asked to determine the point (if any) where the lines described meet, i.e cross one another; we called this the intersection point. There are three popular methods for doing this. They are: (a) substitution, (b) elimination and (c) graphing. In this module we examine the first of these - substitution.

With substitution, you solve one of the equations for one of the variables, and then substitute that quantity into the remaining equation. Let's watch the video to examine the method more closely.

Solving a system using linear elimination involves multiplying each equation by conveniently selected differing constants so that a variable will be eliminated when the equations are added or subtracted. Once a variable is eliminated, we solve for the remaining variable. Let's watch the video to examine the method more closely.

Solving a system via graphing involves plotting the lines on the Cartesian Plane using a calculator and using the Intersect feature to determine where (if at all) the lines have a common point, i.e. they cross (intersect) each other at that point. Let's watch the video to examine the method more closely.