Algebra Course Introduction Welcome to the algebra course! My name is Mike

Algebra Course Introduction

Welcome to the algebra course! My name is Mike and I will be teaching you this course. Algebra, loosely translated from its Arabic roots, means balancing and restoring. But let’s dive deeper into what that means for us. Algebra is like all math, it’s a mystery of the unknown. Before algebra, we do basic arithmetic like adding, subtracting, multiplying, and dividing numbers. However, in algebra, we use variables or unknowns represented by letters like x. The key idea is that variables stand in the place of a number. For example, in the equation x + 1 = 5, x stands in the place of a number. Our goal is to find the number that goes in place of x.

Variables are usually represented by letters of the alphabet, but it doesn’t have to be x. We start with the unknown called the variable x and solve for it. The mysterious nature of algebra makes it a powerful tool. In this course, we’ll see lots of examples and dive deeper into the subject.

Types of Numbers

If you need to memorize the different types of numbers, this is a great place to start. We start with natural numbers, which are sometimes called counting numbers. We start at one and count up from there. If we include zero, sometimes we call them whole numbers. Integers have all the natural numbers, zero, and negative numbers. Rational numbers include all the fractions. Irrational numbers like the square root of 2 and 3 are also real numbers. Complex numbers are real numbers with imaginary numbers.

The real number line is a continuous line of numbers with no holes or gaps. It includes all integers and fractions. The associative property tells us that the grouping of addition and multiplication doesn’t matter. For example, a+b+c is the same as a+(b+c).

Associative and Commutative Properties of Addition and Multiplication

The associative property of addition and multiplication states that the grouping of the numbers does not matter.

For addition: (a + b) + c = a + (b + c)

For multiplication: (a x b) x c = a x (b x c)

The commutative property of addition and multiplication states that the order of the numbers does not matter.

For addition: a + b = b + a

For multiplication: a x b = b x a

The commutative property of addition and multiplication are important in simplifying mathematical expressions.

Simplifying Fractions

The rule for dividing a number by itself is that it is equal to 1, except for 0 divided by 0 which is undefined. This rule is useful in simplifying fractions.

To simplify fractions, divide the numerator and denominator by their greatest common factor. This can be abbreviated by canceling out the common factor.

However, canceling out common factors is only valid for multiplication, not for addition.