# Learning FractionsHub Page

Welcome to the Math Salamanders Learning Fractions support page.

Here you will find information and support about everything to do with fractions.

We have a huge range of resources, from fraction calculators and fraction conversion sheets to fraction information posters, fraction strips and flashcards.

This page contains links to other Math webpages where you will find a range of activities and resources.

If you can't find what you are looking for, try searching the site using the Google search box at the top of each page. ## Online Fraction Calculators

### Fraction Definitions

#### What is a fraction?

A fraction is a number which contains parts of a whole.

Fractions can be smaller than or larger than one (one whole).

A fraction is a number with the form: ${n \over d}$

where n and d are two numbers.

The number n above the line is called the numerator.

The number d below the line is called the denominator.

#### Alternative notation

Alternative ways of expressing this statement include:

n over d, n ÷ d

#### Fraction Notation Example

The fraction ${5 \over 6}$ could be expressed as: five-sixths, five over six, 5 ÷ 6

### Proper and Improper Fractions & Mixed Numbers

A fraction is a number with the form: ${n \over d}$

• If the numerator is smaller than the denominator (if n < d), then the fraction is called a proper fraction, and its value is less than 1.
• If the numerator is greater than the denominator (if n > d), then the fraction is called an improper fraction, and its value is greater than 1.
• If the numerator is equal to the denominator (if n = d), then the fraction's value is equal to 1.
• Please note: if the value of n or d is negative, then we compare the absolute values.

• A mixed fraction (or mixed number) is a number that has a whole number part to it, and a fraction part to it.

### Types of Fractions Examples

${3 \over 7} \; , \; {2 \over 10} \; and \; {17 \over 26}$ are all proper fractions.

${31 \over 5} \; , \; {15 \over 10} \; and \; {37 \over 23}$ are all improper fractions.

$3{1 \over 5} \; , \; 2 {5 \over 8} \; and \; 4 {1 \over 2}$ are all mixed numbers or mixed fractions.

To get help converting improper fractions to mixed numbers,

### "Common" or "Vulgar" Fractions

A common or vulgar fraction is simply an ordinary fraction.

The numerator and denominator must be integers, or whole numbers, and the denominator cannot equal zero.

${35 \over 45} \; , \; {5 \over 9} \; and \; {51 \over 16}$ are all common or vulgar fractions.

${3.2 \over 4.5} \; , \; {5 \over 0} \; and \; {0.57 \over 1.6}$ are NOT common or vulgar fractions.

### Decimal Fractions

A decimal fraction is a fraction where the denominator is a power of ten.

${7 \over 10} \; , \; {5 \over 100} \; , \; {537 \over 1000}$ are all decimal fractions.

They are equal to 0.7, 0.05 and 0.537 respectively.

${3 \over 5} \; , \; {2 \over 12} \; and \; {263 \over 500}$ are not decimal fractions.

### Basic Fraction Arithmetic

Here are the formulas for adding, subtracting, multiplying and dividing two fractions:

${a \over b} + {c \over d} = {ad + bc \over bd}$

Formula for subtracting two fractions

${a \over b} - {c \over d} = {ad - bc \over bd}$

Formula for multiplying two fractions

${a \over b} \times {c \over d} = {ac \over bd}$

Formula for dividing two fractions

${a \over b} \div {c \over d} = {ad \over bc}$

How to add and subtract fractions support

How to multiply and divide fractions support

### Interactive Fraction Builder

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