## Make sure you know these fractions fundamentals

While any level of mathematics is relatively easy once you know the rules, there are a few things to remember about fractions that will keep you out of trouble on school assignments.

Take the time to master these simple reminders and you will never have to worry about them again – the best thing about math is that **the rules are the rules and they don’t change!**

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#### Uniqueness of the Number 1

**Multiplying**any number by 1

**does not change**the value of the number.

**Dividing** any number by 1 **does not change** the value of the number.

**Keep in mind…**

The number 1 can take on many forms. 3 – 2 = 1 and 20 – 19 = 1 can be used as a substitute for the number 1 because they both have a value of 1. **Also…** When the numerator of a fraction is equivalent (equal) to the denominator of a fraction, the overall value of the fraction is 1. This only works when you have a **legal fraction**; that is to say, the denominator **does not equal zero**. You can substitute any of these fractions for the number 1.

**For example…**

**2/2, 5/5, 31/31, etc., are all the equivalent to the number 1.**[/box]

#### Integers Written as a Fraction

**Example:**

**The integer “8” can be expressed as the fraction “8/1” or “16/2” or “32/4” because they all have an overall value equal to “8”.**[/box]

#### Division by Zero

**undefined**.[/box]

#### Zero in the Numerator

**can**have a value of zero. Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of “zero.”[/box]

#### One Minus Sign in a Fraction

**one minus sign**in a simple fraction, the value of the fraction will be

**negative**.[/box]

#### More Than One Minus Sign

**positive**.

If there is an odd number of minus signs in a fraction, the value of the fraction is **negative**[/box]

#### Factoring Integers

**Don’t forget**that the number 1 is the factor of every number (normally the number 1 is omitted). Any factor of a number can be divided evenly into that number.

- Example:
- The factors of the number 12 are 1, 2, 3, 4, 6, 12
- The factors of the number 35 are 1, 5, 7, 35
- The factors of the number 53 are 1, 53, because 53 is a
**Prime Number**.

Here is an easy short-cut method for finding the **prime factors** of a number. Simply divide the number by the lowest possible Prime Number until the final resulting answer is a Prime Number.

**Example:**

**As you can see in the example, the prime factors of 56 are 2 x 2 x 2 x 7**

Keep dividing the resulting number by the smallest prime number that will go into the number evenly. Start with “2” if the number is even. Otherwise start with the lowest prime number possible (3, 5, 7, etc.), until you are left with only a Prime Number.[/box]

#### Reducing Fractions

- Factor the numerator.
- Factor the denominator.
- Cancel-out fraction mixes that have a value of 1.
- Re-write your answer as the reduced fraction.

#### Equivalent Fractions

**equivalent fraction**.

Try to remember this one, because you will use it a lot in other homework assignments.

[/box]#### Simplifying Improper Fractions

**must simplify**your answer. Because, the simplified results will be in the form of a

**mixed number**.

So, to **convert** an improper fraction into a mixed number, just divide the numerator by the denominator. The results will be a whole number part and a fractional part.

#### Greatest Common Factor (GCF)

**two ways**to find the greatest common factor. Remember to follow your homework instructions, if your teacher asks for a particular method.

The **first method** is to list all of the factors of each number, then list the common factors and choose the largest one.

The **second method** is to list the **prime factors**, then multiply the common prime factors…

#### Least Common Multiple (LCM)

**non-zero**whole numbers is actually the smallest whole number that is

**divisible by each**of the numbers. When doing your homework, keep in mind that there are two widely used methods for

**finding the least common multiple**of a group of numbers. [/box]

#### Least Common Denominator (LCD)

Once you know the least common multiple, you would simply re-express each fraction by building an equivalent fraction using the newly named denominator.

[/box]### [icon name=”process” size=”big”] Homework Helpers

These great tips will really **simplify your fractions homework**. Click here > [/column] [column width=”1/2″ last=”yes”]

### [icon name=”plus” size=”big”] How to Do Fractions

**Tutorials** on how to add, subtract, multiply and divide fractions! Click here to start with adding > [/column] [column width=”1/2″ first=”yes”]

### [icon name=”phone” size=”big”] Fraction Calculator

Learn how to solve fraction problems, then check your work with our online **fraction calculator**. Click here > [/column] [column width=”1/2″ last=”yes”]

### [icon name=”pencil” size=”big”] Fraction Worksheets

**Free downloadable worksheets** give you tons of practice to learn how to solve fraction problems. Click here > [/column] [line]