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!
Uniqueness of the Number 1
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.
2/2, 5/5, 31/31, etc., are all the equivalent to the number 1.[/box]
Integers Written as a Fraction
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
Zero in the Numerator
One Minus Sign in a Fraction
More Than One Minus Sign
If there is an odd number of minus signs in a fraction, the value of the fraction is negative[/box]
- 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.
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]
- Factor the numerator.
- Factor the denominator.
- Cancel-out fraction mixes that have a value of 1.
- Re-write your answer as the reduced fraction.
Try to remember this one, because you will use it a lot in other homework assignments.[/box]
Simplifying Improper Fractions
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.[/box]
Greatest Common Factor (GCF)
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…[/box]
Least Common Multiple (LCM)
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
[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]