Properties of Fractions


a fraction of the wholeMany of my students are afraid of fractions, but they are very useful in algebra and upper levels of math. They can actually make the problem easier to solve and they frequently make more sense than decimals.

X over Y fractionIn algebra, teachers can tell if you are using a calcultor for solving all your problems because you give your answer in decimals instead of fractions. If you absolutely cannot do fractions then I strongly suggest you get a calculator that can do fractions for you. If you don't plan to study a lot of math in college, try the TI-15 for about $15. If you are college bound, then try a TI-Nspire or TI-Nspire CAS for around $150.The TI-84 now has a fraction function, and it is priced around $130 or, if you already have a TI-84, you can download the upgraded operating system that does froctions for free from the TI website.

In common usage, a fraction is a part of a unit. In mathematics, a fraction is a quotient (divide problem) or a ratio. In common usage and lower levels of math, improper fractions must be changed to a mixed number. But in algebra and high levels of math, an improper fraction can have more meaning and can actually be the preferred answer.


Fraction Definitions

a fraction of the wholeMost schools teach students about common fractions. These consist of a numerator and a denominator (for example or ).

The numerator, the top part of the fraction, represents a number of equal parts. The denominator, the bottom part of the fraction, tells how many of those parts make up a whole. An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole.

A proper fraction is a fraction where the numerator is smaller than the denominator. An improper fraction is one where the numerator is larger. The can be converted into a mixed numer consisting of a whole numer part and a fraction part.

The reciprocal or multiplicative inverse of a fraction is the the fraction that can be multiplied by the original with the answer equal to one (1). For example: 2/3 x 3/2 = 1, so 2/3 and 3/2 are reciprocals.


Math Properties for Adding Fractions

Math Property

Meaning of Property and Example

Closure Property for Fraction Addition The sum of two fractions is a fraction.
Commutative Property for Fraction Addition The order in which two fractions are added does not affect the sum (answer).
Associative Property for Fraction Addition The sum of three fractions is the same no matter how you group the fractions.
Additive Identity Property of Zero for Fraction Addition Zero added to any number is the number itself.
Additive Property of Equality If you add equal amounts to both sides of an equation, the equation is still equal.
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Math Properties for Multiplication of Fractions

Math Property

Meaning of Property and Example

Closure Property for Fraction Multiplication The product of any two fractions is a fraction.
Commutative Property for Fraction Multiplication The order in which two fractions are multiplied does not affect the product (answer).
Associative Property for Fraction Multiplication The product of three fractions is the same no matter how you group the fractions.
Multiplicative Identity Property for Fraction Multiplication One multiplied by any number is the number itself.
Multiplicative Inverse Property for Fraction Multiplication For every nonzero fraction b/a there is a unique fraction a/b such that b/a x a/b = 1
Distributive Property for Fraction Multiplication over Addition or Subtraction If a term is multiplied by terms in parenthesis, we need to "distribute" the multiplication over all the terms inside.
Multiplicative Property of Equality If you multiply equal amounts by everything on both sides of an equation, the equation is still equal.

Density Property of Fractions

Between any two fractions on a number line, there is always a fraction between them.

fraction bars

Comments, questions, or you just need some help? Send an e-mail to Mrs. Shearer Last Updated: 02/04/2011
K. A. Shearer 2010-2011
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