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Understanding the Rules for Fractions

written by: Kathy Foust • edited by: SForsyth • updated: 1/5/2012

Improve your grades on math tests and homework by understanding the rules for fractions. This guide covers adding, subtracting, multiplying and dividing fractions, along with other tricky subjects.

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    The Basics of Fractions

    A fraction states how many parts are in a whole. The top number is called a numerator and the bottom number is called a denominator. Simply put, the numerator is how many parts out of the denominator so that if you have a fraction that says 1/2,what it is really saying is "one out of two". The two makes up the "whole" while the one makes up the "parts of the whole". If you can remember that then you have already won half the battle! Read the rules and explanations of them below to increase your understanding of fractions and how to use them.

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    Fraction Rules

    Below is a list of fraction basics as well as explanations for each rule.

    • If the numerator remains the same for all fractions but the denominator gets larger, the actual value of the fraction gets smaller. This fraction rule is because of the fact that if the denominator increases then the whole is divided into more parts. Imagine your favorite cookie. You have to share it with your sister. Would you want 1/2 of the cookie or would you want 1/10 of the cookie? You want 1/2 of course because it's going to be a bigger piece!
    • When adding or subtracting fractions, the denominator must be the same for both fractions in order to perform the operation. This rule makes sense because you cannot add fractions from different groups. For instance, you cannot add 1/2 and 1/4 because they represent different groups.
    • When adding or subtracting fractions, the denominator remains the same while the actual mathematical operation is performed on the numerator. You are working with parts of the whole. Therefore the whole doesn't change, only the parts do. So 2/4 added to 1/4 would equal 3/4. See how the numerator changed but the denominator didn't?
    • Since the denominators have to be the same in order to perform addition and subtraction, you sometimes have to change the fraction. The only way to add numbers like 1/4 and 1/2 is to make the denominators the same. To do so, you need to multiply 1/2 by 2/2. When you change fractions, you must do to the top what you do to the bottom. You aren't actually changing the value of the fraction, just the way it is written. 1/2 will become 2/4 when multiplied by 2/2.
    • When multiplying fractions, numerators multiply with numerators and denominators multiply with denominators. For example, 2/4 times 3/1 would mean 2 times 3 and 1 times 4. Your answer would be 6/4.
    • Any fraction that has a "1" as a denominator can be rewritten as a whole number using the numerator. For example 6/1 can be written as "6" because you are actually saying that out of 1 part, you have 6.
    • Any fraction that has the same number as a numerator and as a denominator can actually be written as one, no matter how big or small the numbers are. For instance, 1/1 is the same as 999/999. The fractions here are simply saying that you have all the parts of a whole.
    • Fractions can be used as division problems. 2/4 means 2 divided by 4. The top number (numerator) is always divided by the bottom number (denominator).

    These are some of the basic rules of fractions. Using these rules will help you to understand the basic concept of fractions and will greatly benefit you as you work your way into more difficult concepts in fractions. No matter how difficult the mathematical equations get, these rules for fractions will always apply!