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### Using Prime Factorizations

Every whole number greater than 1 has a *prime factorization* — that is, the list of prime numbers (including repeats) that equal that number when multiplied together. For example, here are the prime factorizations [more…]

### Introducing the Percent Circle

The *percent circle* is a simple visual aid that helps you make sense of percent problems so that you can solve them easily. The trick to using a percent circle is to write information into it. For example [more…]

### Using Probability to Calculate the Odds in the Game of Craps

*Probability* is the mathematics of deciding how likely an event is to occur. You can calculate the probability of an event by using the following formula: [more…]

### Simplifying and Factoring Expressions

In algebra, simplifying and factoring expressions are opposite processes. *Simplifying an expression* often means *removing* a pair of parentheses; *factoring an expression* [more…]

### 10 Math Concepts You Can't Ignore

Math itself is one big *concept,* and it's chock full of so many smaller mathematical concepts that no one person can possibly understand them all — even with a good dose of studying. Yet certain concepts [more…]

### How to Convert between Fractions and Repeating Decimals

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number), using either calculator or pencil and paper. For example, here’s how to convert the fraction [more…]

### Making Sense of Weird Exponents

Exponents are a quick way to represent repeated multiplication. Raising a *base* number to the power of an *exponent*means multiplying the base by itself the number of times indicated by the exponent. For [more…]

### Solving Systems of Equations in Algebra

In most cases, an algebraic equation is solvable only when one value is unknown — that is, when the equation has only one variable. In rare cases, you can solve an equation with two or more variables because [more…]

### 10 Great Mathematicians

Mathematics is an ongoing journey of thousands of years and millions of minds. The list below is by no means complete, but here are ten great mathematicians whose work forever changed not only math but [more…]

### Inverse Operations and the Commutative Property

The Big Four operations — addition, subtraction, multiplication, and division — are actually two pairs of *inverse operations,* which means that the operations can undo each other: [more…]

### How to Divide Big Numbers with Long Division

To divide larger numbers, use *long division.* Unlike the other Big Four operations, long division moves from left to right. For each digit in the *dividend* [more…]

### How to Multiply Multiple Digits

To multiply large numbers, stack the first number on top of the second. Then multiply each digit of the bottom number, from right to left, by the top number. In other words, first multiply the top number [more…]

### How to Line Up Columns in Addition and Subtraction

To add or subtract large numbers, stack the numbers on top of each other so that all similar digits (ones, tens, hundreds, and so forth) form columns. Then work from right to left. Do the calculations [more…]

### The Number Line and Addition, Subtraction, Multiplication, and Division

The *number line* is just a line with numbers marked off at regular intervals. You probably saw your first number line when you were learning how to count to ten. You can use this trusty tool to perform [more…]

### How to Round Numbers Up and Down

Rounding numbers makes long numbers easier to work with. To round a two-digit number to the nearest ten, simply increase it or decrease it to the nearest number that ends in 0: [more…]

### How to Identify the Place Value Digits within Numbers

*Place value* assigns each digit in a number system a greater or lesser value depending upon where it appears in a number. The number system used most commonly throughout the world is the Hindu-Arabic number [more…]

### 10 Curious Types of Numbers

Numbers seem to have personalities all their own. For example, even numbers are go-along numbers that break in half so you can carry them more conveniently. Odd numbers are more stubborn and don't break [more…]

### 10 Alternative Numeral and Number Systems

The distinction between numbers and numerals is subtle but important. A number is an idea that expresses how much or how many. A numeral is a written symbol that expresses a number. Here are ten ways to [more…]

### 10 Important Number Sets to Know

Each of the sets of numbers listed here serves a different purpose, some familiar (such as accounting and carpentry), some scientific (such as electronics and physics), and a few purely mathematical. [more…]

### How to Multiply Quickly with Exponents

You can multiply very quickly when you understand the concept of exponents. Here's an old question whose answer may surprise you: Suppose you took a job that paid you just 1 penny the first day, 2 pennies [more…]

### The Basic Concept of Negative Numbers

When people first find out about subtraction, they often hear that you can't take away more than you have. For example, if you have four pencils, you can take away one, two, three, or even all four of [more…]

### How to Visualize Fractions on a Number Line

Fractions help you fill in a lot of the spaces on the number line that fall between the counting numbers. For example, the figure shows a close-up of a number line from 0 to 1. [more…]

### 4 Important Sets of Numbers

The number line grows in both the positive and negative directions and fills in with a lot of numbers in between. Here is a quick tour of how numbers fit together as a set of nested systems, one inside [more…]

### How to Tell the Difference between Numbers and Digits

Sometimes people confuse numbers and digits. The number system you're most familiar with — Hindu-Arabic numbers — has ten familiar digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For the record, here's the difference [more…]

### How to Count Beyond Ten with Place Value

The ten digits in the number system allow you to count from 0 to 9. All higher numbers are produced using place value. Place value assigns a digit a greater or lesser value, depending on where it appears [more…]