# 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).

#### What do fractions look like?

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, n ÷ d

#### Fraction Notation Example

The fraction ${5 \over 6}$ could be expressed as:

• five-sixths
• five over six
• 5/6
• 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.
• A mixed fraction (or mixed number) is a number that has a whole number part to it, and a fraction part to it.

Please note: the comparisons between the numerator and denominator above assume that they are both positive numbers. If either n or d is negative, then we need to compare their absolute values to find outwhether the fraction is a proper fraction or an improper fraction

### Types of Fractions Examples

${3 \over 7} \; , \; {2 \over 10} \; , \; -{3 \over 5} \; and \; {17 \over 26}$ are all proper fractions.

${31 \over 5} \; , \; {15 \over 10} \; , \; -{17 \over 3} \; and \; {37 \over 23}$ 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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