Online Calculators since 2009
The Ordering Fractions Calculator is a free online calculator that allows you to place a set of fractions into their size order. The ordering fractions calculator can order the fractions by the Least to the Greatest amount and by the Greatest to the Least amounts. The Ordering Fractions Calculator is a great tool for calculating fractions to help check with homework answers and/or prepare for exams. You can enter vulgar fraction into the Ordering Fractions Calculator and decimal fractions. The Ordering Fractions Calculator can calculate vulgar fractions and decimal fractions separately or both combined (ie 1/2, 3/4 , 0.5, 0.75).
|Order from Least to Greatest|
In math terms, a fraction is a numerical quantity that is not a whole number. 1, 2, 3 etc. are whole numbers. In mathematics, whole numbers are also referred to as 'integers' and/or 'natural numbers'. Please note that this can be a little confusing as integers are only whole numbers if they are positive integers.
So, a fraction is not a whole number. A whole number can be defined as:
A whole number is a positive number that is NOT a fraction, is not a percentage and is not a decimal number.
The difference between a whole number and an integer is that Integers can contain minus numbers
Let's look at an example: if we look at the table below, we can see that integers can be whole numbers when they are Positive Integers (that is, they are greater than zero) but not all integers are whole numbers (when an integer is less than or equal to zero, it is not a whole number).
|Negative Integer||Positive Integer|
|and Less -9 -8 -7 -6 -5 -4 -3 -2 -1 0||1 2 3 4 5 6 7 8 9 and more|
So, we know that we can define a fraction as a numerical quantity that is not a whole number but, what does that mean in simple terms. Well, in simple terms a fraction is an equal part of an object or for math, part of a number. An easy way to think of this is a cake.
Lets imagine you are having a birthday. You buy a nice round birthday cake. This is one (1) cake.
You have 8 friends coming to your birthday party, so you cut the cake into sixteen parts. You do this by cutting the cake down the middle. This gives you 2 pieces of cake. You then cut those two pieces down the middle. This gives you 4 pieces of cake. You finally cut the 4 pieces along the middles to get 8 pieces of birthday cake. The important word here, is pieces. We have 8 pieces of cake that, when together, form a whole cake. Let's look at how we express our example in math terms, this will also help us to later explain how fractions are written down.
|Number of Pieces||fraction|
Our table above highlights how we write a fraction. This method of writing a fraction is called a vulgar fraction or common fraction.
A Vulgar Fraction (or Common Fraction) is a fraction expressed by a numerator and a denominator (not decimally), the two numbers being separated by the Vinculem.
In simple terms a Vulgar fraction or Common Fraction is one number written above another, separated by a line. In mathematics, the two numbers in a fraction have special names, so does the line that separates the top and bottom number.
The number at the top of a fraction is called a Numerator
The number at the top of a fraction is called a Denominator
The line in a fraction that separates the top number (Numerator) and bottom number (Denominator) is called a Vinculem.
A Decimal Fraction is a Vulgar Fraction where the denominator is a power of 10 (10, 100, 1000, 10000, 100000, etc.).
Decimal numbers can be expressed as a Vulgar Fraction or as a decimal number. This is particularly useful when adding, subtracting, multiplying and dividing fractions.
Ordering fractions is the process of placing multiple Vulgar Fractions and/or Decimal Fraction into an order based on their relative size (Least to Greatest or Greatest to Least).
So, we now know that there are Vulgar Fractions and Decimal Fractions. We also know that decimal fractions are fairly easy to work with for addition, subtraction, multiplication and division. We can also use the online Ordering Fractions Calculator to work with our fractions and test our results. Let's now look at how we manually Order Fractions
Vulgar Fractions can be placed into order by:
Here are some of our other Fraction calculators which you will find useful, these further discuss the calculation of Common Fractions using the Common Denominator and fraction cross multiplication.
You may also find the following Math calculators useful.