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### 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 Check an Answer to an Algebra Problem

Checking your answers when doing algebra problems is always a good idea — after all, if there's a way to ensure that you have the correct answer, it's worth the time, isn't it? You check your answers in [more…]

### How to Work with Coefficients

Algebra simplifies expressions with coefficients*,* which are numbers preceding variables. For example, 3 is the coefficient in 3*x*. 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…]

### Combining Square Roots

Square roots, which use the radical symbol, are nonbinary operations — operations which involve just one number — that ask you, “What number times itself gives you this number under the radical?” Finding [more…]

### Basics of Positive and Negative Numbers

Positive and negative numbers are all integers. Integers are whole numbers that are either greater than zero (positive) or less than zero (negative). For every positive integer, there's a negative integer [more…]