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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…]


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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Graph an Area Where Inequalities Overlap

You can find the solution of a system of inequalities involving a line and a curve (such as a parabola), two curves, or any other such combination.

You do this by graphing the individual equations, determining [more…]


Apply Additive and Multiplicative Identities in Algebra

The numbers zero and one have special roles in algebra — as additive and multiplicative identities, respectively. You use identities in algebra when solving equations and simplifying expressions. [more…]


The Multiplication Property of Zero

The multiplication property of zero is really useful for doing algebra. Of course, you may be thinking that multiplying by zero is no big deal. After all, zero times anything is zero, right? Well, that's [more…]


Simplify Linear Algebraic Equations by Removing Fractions

The problem with fractions in linear algebraic equations is that they aren't particularly easy to deal with. For example, they always require common denominators before you can add or subtract them. [more…]


Isolate an Unknown Variable in an Algebraic Equation

Life isn't always as easy as one-variable equations. Being able to solve an algebra equation for some variable when it contains more than one unknown can be helpful in many situations. [more…]

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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…]

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…]

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…]

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…]

Algebra Equations for Multiplying Binomials

In algebra, multiplying binomials is easier if you recognize their patterns. You multiply the sum and difference of binomials and multiply by squaring and cubing to find some of the special products in [more…]

Algebra’s Quadratic Formula

You can find solutions for quadratic equations by factoring, completing the square, guessing, or everyone's favorite — using the quadratic formula. The best thing about the quadratic formula [more…]

Rules for Radicals — the Algebraic Kind

Working with radicals can be troublesome, but these equivalences keep algebraic radicals from running amok. Finding the root of product or quotient or a fractional exponent is simple with these formulas [more…]

Algebra’s Laws of Logarithms

Logarithms help you add instead of multiply. The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal, base, and the log of 1. [more…]

How to Multiply Two Mixed Numbers

Knowing how to multiply fractions will help when it comes to multiplying two mixed numbers. This is because when multiplying mixed numbers, you first have to change them to improper fractions. You then [more…]

How to Multiply Three Mixed Numbers

Multiplying mixed numbers is quite similar to multiplying simple fractions. Sometimes, you may need to multiply three or more mixed numbers together, for example, when applying one discount after another [more…]

How to Remember the Order of Operations

You have to follow the order of operations with each algebra problem you solve. Following the order of operations in algebra ensures that anyone reading a mathematical expression can solve it the same [more…]

How to Determine What Variables Represent

Algebra uses letters, called variables,to represent numbers that correspond to specific values. Algebraic variables can represent the unknown and what you’re solving for in an algebra problem, as well [more…]

How to Change Improper Fractions to Mixed Numbers

Changing improper fractions to mixed numbers can help you better understand the result of an algebraic problem. Improper fractions are simply top-heavy fractions whose numerators [more…]

How to Create Equivalent Fractions Using Common Denominators

You must find a common denominator if you want to add, subtract, or compare fractions that have different denominators. A common denominator, which means having the same number in the denominator [more…]

Grouping Symbols in Algebra

Grouping symbols organize an algebra problem that contains multiple groups. Algebraic grouping symbols — parentheses, brackets, braces, radicals, and fraction lines — show where a group starts and ends [more…]

How to Determine Absolute Value

In algebra, the absolute value operation tells you how far a number is from zero. It doesn’t pay any attention to whether the number is less than or greater than zero, and so absolute values are always [more…]

How to Add Positive and Negative Numbers with the Same Sign

If you add a positive number with another positive number, the sum is always a positive number; if you add two negative numbers, the sum is always a negative number. So when you have an algebra problem [more…]

Recognizing Operational Symbols in Algebra

The basics of algebra involve symbols. Algebra uses symbols for quantities, operations, relations, or grouping. The symbols are shorthand and are much more efficient than writing out the words or meanings [more…]

How to Solve Algebra Problems with Grouping Symbols

Grouping symbols organize an algebra problem that contains multiple groups. These grouping symbols — parentheses (), brackets [], braces {}, radicals (the square root symbol), and fraction lines — show [more…]

Recognizing Relationship Symbols in Algebra

Algebraic relationship symbols show how numbers or terms of an equation relate to each other. The relationship symbols show if one value is larger, smaller, equal, or approximately equal to another value [more…]

How to Distribute Variables

Distributing variables over the terms in an algebraic expression involves multiplication rules and the rules for exponents. When different variables are multiplied together, you can write them side by [more…]

How to Add Positive Numbers with Negative Numbers

When the signs of two numbers that you're adding are different, forget the signs and find the difference between the numbers — which is the difference between their absolute values. The number farther [more…]

How to Subtract Positive and Negative Numbers

Subtracting positive and negative numbers is really easy to do: You don’t! Just change the minus sign (the one that's the operator) to a plus sign, change the number that the minus sign was in front of [more…]

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…]