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Algebra

Featured Articles

Algebra

How to Add and Subtract with Powers

To add or subtract with powers, both the variables and the exponents of the variables must be the same. You perform the required operations on the coefficients, leaving the variable and exponent as they are. When adding or subtracting with powers, the terms that combine always have exactly the same variables with exactly the same powers. [more…]

Algebra

How to Write Numbers in Scientific Notation

Scientific notation is a standard way of writing very large and very small numbers so that they're easier to both compare and use in computations. [more…]

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Algebra Basics

How to Use the Order of Operations

Follow the order of operations with each algebra problem you solve. The order of operations in algebra is important if you want to find the correct answer. You first work through any grouping symbols, [more…]

Quadratics in Algebra

Standard Equations of Algebraic Conics

Conics are curved algebraic forms that come from slicing a cone with a plane. Use these equations to graph algebraic conics, such as circles, ellipses, parabolas, and hyperbolas: [more…]

Linear Equations in Algebra

Cramer’s Rule for Linear Algebra

Named for Gabriel Cramer, Cramer’s Rule provides a solution for a system of two linear algebraic equations in terms of determinants — the numbers associated with a specific, square matrix. [more…]

Counting Techniques

Algebraic Permutations and Combinations

In algebra, you use permutations to count the number of subsets of a larger set. Use permutations when order is necessary. With combinations, you can count the number of subsets when order doesn't matter [more…]

Algebra Basics

Eight Basic Algebraic Curves

Algebra is all about graphing relationships, and the curve is one of the most basic shapes used. Here's a look at eight of the most frequently used graphs. [more…]

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How to Multiply and Divide Positive and Negative Numbers

Multiplying and dividing positive and negative numbers is a simple operation with two numbers. With three or more, it is also straightforward, but you use the Even-Odd Rule. [more…]

How Zero Affects Positive and Negative Numbers

It isn’t too tricky to perform operations using positive and negative numbers with zero. You follow normal addition and subtraction rules, and what zero does to the final sign depends on where the zero [more…]

How to Reorder Operations with the Commutative Property

The commutative property makes working with algebraic expressions easier. The commutative property changes the order of some numbers in an operation to make the work tidier or more convenient — all without [more…]

How to Apply the Associative Property

The associative property comes in handy when you work with algebraic expressions. Use the associative property to change the grouping in an algebraic expression to make the work tidier or more convenient [more…]

How Fractions Are Put Together

Fractions just have two parts: a numerator and a denominator. The denominator, or bottom number, indicates the total number of items. The numerator, or top number, tells you how many of the total [more…]

How Proper Fractions Work

The simplest type of fraction is a proper fraction, which is always just part of one whole thing. In a proper fraction, the numerator is always smaller than the denominator, and its value is always less [more…]

What to Do When Fractions Don't Reduce

It’s always nice when you can reduce a fraction to make it more user-friendly. The fraction 3/4 is much nicer than 447/596. Sometimes, though, the fraction just doesn’t want to cooperate. In these cases [more…]

How to Divide Fractions

Dividing fractions is as easy as pie! In fact, after you change mixed numbers to improper fractions, dividing fractions is just like multiplying fractions, except that you flip the numerator and the denominator [more…]

How to Convert Decimals to Fractions

Converting decimals into fractions isn't hard. To convert a decimal into a fraction, you put the numbers to the right of the decimal point in the numerator [more…]

How to Convert Fractions to Decimals

You can convert all fractions to decimals. The decimal forms of rational numbers either end or repeat a pattern. To convert fractions to decimals you just divide the top by the bottom — divide the numerator [more…]

Using Exponents to Simplify Equations

An exponent is a small, superscripted number written above and to the right of a larger number, the base — this tells you how many times you multiply the base by itself. This repeated multiplication is [more…]

How to Write Numbers in Scientific Notation

Scientific notation is a standard way of writing very large and very small numbers so that they're easier to both compare and use in computations. To write in scientific notation, follow the form [more…]

How to Multiply Exponents

You can multiply many exponential expressions together without having to change their form into the big or small numbers they represent. When multiplying exponents, the only requirement is that the bases [more…]

How to Divide Exponents

You can divide exponential expressions, leaving the answers as exponential expressions, as long as the bases are the same. To divide exponents (or powers) with the same base, subtract the exponents. Division [more…]

How to Divide with the Power of Zero

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How to Work with Coefficients

Algebra simplifies expressions with coefficients, which are numbers preceding variables. For example, 3 is the coefficient in 3x. Rather than using a multiplication sign between 3 and [more…]

How to Add and Subtract Variables

Whether you add or subtract variables, you follow the same rule, even though they have different operations: when adding or subtracting terms that have [more…]

How to Add and Subtract with Powers

To add or subtract with powers, both the variables and the exponents of the variables must be the same. You perform the required operations on the coefficients, leaving the variable and exponent as they [more…]

How to Multiply Variables

When variables are the same, multiplying them together compresses them into a single factor (variable). But you still can’t combine different variables. When multiplying variables, you multiply the coefficients [more…]

Dividing Variables in Algebra

Dividing variables in an algebra problem is fairly straightforward. Each variable is considered separately. The number coefficients are reduced the same as in simple fractions. When dividing variables, [more…]

Identifying Prime Numbers

A prime number is a whole number larger than the number 1 that can be divided evenly only by itself and 1. The first and smallest prime number is the number 2. It’s the only even prime number. All primes [more…]

How to Write Prime Factorization of Composite Numbers

Prime factorization shows you the only way a number can be factored. The process of prime factorization breaks down a composite number into the prime numbers that, when multiplied together, give you that [more…]

How to Reduce Fractions Using Prime Factorization

You can use prime factorization to reduce fractions. Start with numbers only and then add variables (letters that represent any real number) to the mix. The beauty of using the prime factorization method [more…]

How to Perform Distribution in Algebra

Distributing items is an act of spreading them out equally. Algebraic distribution means to multiply each of the terms within the parentheses by another term that is outside the parentheses. To distribute [more…]

How to Distribute Positive and Negative Numbers

When performing distribution, be aware of the sign being distributed and how that sign affects each term. Distributing a positive sign makes no difference in the signs of the terms — the signs stay the [more…]

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