What are the basics of algebra?

Answer 1

First, to understand the basics of Algebra you should be familiar with the following operations:

• Addition and
• Multiplication and
• Division and
• Subtraction of fractions and decimals.

Generally most people prepare by taking Pre-Algebra which covers all the basics necessary to begin Algebra.

Most people begin by learning some terms that are common in Algebra. Those are:

• Algebraic Expression - any expressed phrase containing an infinite number of numbers or variables and has at least one operation (addition, subtraction, multiplication, or division).

1. An example: 4x + 3x, It contains numbers, variables and has one operation. Notice there is no equal sign.

Now Algebraic Expressions are composed of, Terms.

1. An example: 4x is a term, 3x is a term. In the Algebraic Expression,

   45x² ÷ 16y² - √51, with 45x², 16y², √51, all being terms. Even the number 1 is a term.

A term can have, a coefficient, a constant, and a variable. A coefficient is the first number in a term. A constant is a single number with no variable attached. An a variable is a letter, as it can "vary" - hence the term variable.

1. An example: The term 4x contains both a coefficient (4) and a variable (x). In the equation, 4x + 1 = 6, the 1 and 6 are both constants. The random letters "ab", "x", "y", etc are variables.

As mentioned above Algebraic Expressions do not have equal signs, that's because If any set of algebraic expressions contain an equal sign, this defines an Equation.

1. An example: 4x + 3x = 14.

You may be asked to solve an Algebraic Sequence.

1. An example: (5, 20, 35, 50, 65 ....).

The above example calls for finding the missing number. If you're good in the basics of math you'd eventually see the pattern is +15 to each number.

You will also learn that there are different types of Numbers. There are:

• Real Numbers - are exactly that, a real number. It can be plotted on a number line. A fraction, decimal, integers (negative and positive) temperature, etc are all real numbers. There are non real numbers, but those are learned about in college level Algebra.

1. An example: 6/10, 0.6, 60 Degrees

• Rational Numbers - are numbers that can form ratios. Meaning it can be expressed as the quotient of two numbers.

1. An example: 14 (since it's 14/1), 0.164578 (164578/1000000)

• Irrational Numbers - it's exactly the opposite of a rational number. These numbers cannot be expressed as the quotient of two numbers. This is generally reserved for non terminating decimal that do not repeat.

1. A very good example of this is Pi. It continues on forever with the number changing with every place value. 3.14159268

You will need the understand that Algebra does not operate exactly as Arithmetic. In arithmetic you add, subtract, multiply, and divide straight across. In Algebra things have be done in an order. This is called the Order of Operations.

You must follow the order of:

• Brackets
• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

When you're dealing with equations they're generally broken into:

• Monomial
• Binomial
• Trinomial
• Polynomial

A monomial is an equation or expression consisting of one term.

• 4x is a monomial
• 4x + 4x is also a monomial because if we combine like terms (like terms are considered any terms that share a common variable, coefficient, or constant) we're left with 8x.

A binomial is an equation or expression consisting of two terms.

• 4x + 4y is a binomial
• 4x + 4y + 5y + 6x is also a binomal because if we combine like terms we result in 10x + 9y.

A trinomial is an equation or expression consisting of three terms.

• 4x + 4y + 4z is a trinomial
• 4x + 4y + 4z + 5x + 5y + 5z is also a trinomial because if we combine like terms we result in 9x + 9y + 9z.

And lastly, a Polynomial is an equation or expression consisting of four or more terms.

• 4w + 4x + 4y + 4z is a polynomial