## 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

[box color=”blue”]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

[box color=”blue”]You can express any integer as a fraction by simply dividing by 1, or you can express any integer as a fraction by simply choosing a numerator and denominator so that the overall value is equal to the integer.

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

[box color=”blue”]The denominator of a fraction cannot have the value zero. If the denominator of a fraction is zero, this is not a legal fraction because it’s overall value is undefined.[/box]

#### Zero in the Numerator

[box color=”blue”]The numerator of a fraction 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]

[box color=”blue”]If there is one minus sign in a simple fraction, the value of the fraction will be negative.[/box]

#### More Than One Minus Sign

[box color=”blue”]If there is an even number of minus signs in a fraction, the value of the fraction is positive.

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

#### Factoring Integers

[box color=”blue”]To factor an integer, simply break the integer down into a group of numbers whose product equals the original number. 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

[box color=”blue”] To reduce a fraction, follow the following three steps:

1. Factor the numerator.
2. Factor the denominator.
3. Cancel-out fraction mixes that have a value of 1.
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#### Equivalent Fractions

[box color=”blue”]Finding an equivalent fraction (also called building fractions) is the reverse of reducing the fraction. Instead of searching for the 1 in a fraction mix so that you can reduce, you insert a 1 and build. The resulting fraction is called an equivalent fraction.

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

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#### Simplifying Improper Fractions

[box color=”blue”] You may remember from other homework assignments that an improper fractions is where the numerator has a greater value than that of the denominator. So each time you do a math operation on fractions and your answer ends up as an improper fraction, you 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.

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#### Greatest Common Factor (GCF)

[box color=”blue”]The greatest common factor of two or more whole numbers is the largest whole number that divides evenly into each of the numbers. There are 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…

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#### Least Common Multiple (LCM)

[box color=”blue”]The least common multiple of two or more 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.

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#### Least Common Denominator (LCD)

[box color=”blue”]The least common denominator of a fraction is another way of stating the least common multiple of two or more different denominators. They mean the same. So, if you can find the least common multiple of two or more numbers, you can find the least common denominator.

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

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