# Properties of Fractions

Many 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.

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

Most schools teach students about common fractions. These consist of a numerator and a denominator (for example ½ or ¾).

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.

## 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.

Comments, questions, or you just need some help? Send an e-mail to Mrs. Shearer Last Updated: 02/04/2011
The text passage provides definitions and properties of fractions, including common usage, mathematical definitions, and various properties for addition and multiplication of fractions. It does not contain any specific mathematical questions or answers.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

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TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# Properties of Fractions

Many 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.

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

Most schools teach students about common fractions. These consist of a numerator and a denominator (for example ½ or ¾).

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.

## 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.

Comments, questions, or you just need some help? Send an e-mail to Mrs. Shearer Last Updated: 02/04/2011
user
The text passage provides definitions and properties of fractions, including common usage, mathematical definitions, and various properties for addition and multiplication of fractions. It does not contain any specific mathematical questions or answers.

TYPE: NO_QUESTION