Ordering Fractions Calculator

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).

Ordering Fractions Calculator
Ordering Fractions Calculator Results
Order from Least to Greatest
[ 1 Votes ]

How to Order Fractions from Least to Greatest

  1. Enter your fractions into the Ordering Fractions Calculator. Fractions can be entered by typing the Numerator (top number of the fraction), then a forward slash (a forward slash is used to represent the Vinculem) and finally the Denominator (bottom number of a fraction). For example ½ is the same as 1/2 Alternatively, you can enter decimal numbers as a means of expressing the fraction.
  2. Enter all fractions that you want to order from Least to Greatest. Ensure you separate each fraction with a comma. For example 3/8, 1/9, 6/7
  3. Once you have entered all your fractions, click 'Order from Least to Greatest'
  4. The Ordering Fractions Calculator will then order the fractions from Least to Greatest

How to Order Fractions from Greatest to Least

  1. Enter your fractions into the Ordering Fractions Calculator. Fractions can be entered by typing the Numerator (top number of the fraction), then a forward slash (a forward slash is used to represent the Vinculem) and finally the Denominator (bottom number of a fraction). For example 1/2 is the same as ½
  2. Enter all fractions that you want to order from Greatest to Least. Ensure you separate each fraction with a comma. For example 1/2, 3/4, 6/7
  3. Once you have entered all your fractions, click 'Order from Greatest to Least'
  4. The Ordering Fractions Calculator will then order the fractions from Greatest to Least
Ordering Fractions Calculator

What is a Fraction?

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.

What is the difference between a Whole Number and an Integer?

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).

Whole Numbers V's Integer
Negative IntegerPositive Integer
and Less -9 -8 -7 -6 -5 -4 -3 -2 -1 01 2 3 4 5 6 7 8 9 and more
Whole Number

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.

Fraction example - sharing the 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.

Understanding Fractions - The Cake Example
Number of Piecesfraction
11
2½
4¼
8

Our table above highlights how we write a fraction. This method of writing a fraction is called a vulgar fraction or common fraction.

What is a Vulgar 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.

What is the number at the top of a fraction called?

The number at the top of a fraction is called a Numerator

What is the number at the bottom of a fraction called?

The number at the top of a fraction is called a Denominator

What is the line in a fraction called?

The line in a fraction that separates the top number (Numerator) and bottom number (Denominator) is called a Vinculem.

What is a Decimal Fraction?

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.

What is ordering 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).

How do I Calculate the Order of Mixed Fractions?

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:

  1. Using a Common Denominator
  2. Using Cross Multiplication

More Fraction Calculators

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.

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