Order Fractions Game

Order Fractions Game
In this game, your goal is to arrange a set of fractions from the smallest value to the largest value. Scroll down for a detailed explanation.
 

 

How to Play the Order Fractions Game

1. Choose Your Level
   On the Main Menu, select one of two difficulty modes:
   Same Denominators:
   Every fraction has the same bottom number. To order these, you only need to look at the top numbers (numerators).
   Different Denominators:
   Each fraction has a different bottom number. You’ll need to think about how large each piece is (for example, 1/2 is much larger than 1/10) or use one of the comparing fractions techniques.
   

2. Arrange the Fractions
   Once the game starts, you will see four “Fraction Cards” appear in a random order.
   Drag and Drop:
   Use your mouse (or finger on a touchscreen) to click and hold a fraction card.
   Reorder:
   Move the card to a new position in the line.
   The Goal:
   Arrange them so the Smallest value is on the Far Left and the Largest value is on the Far Right.
   

3. Check and Advance
   Check Order:
   Click this button when you think you have them in the right sequence. The game will tell you if you are correct or if you need to try swapping some cards.
   New Set:
   Click this to get a brand-new group of fractions to practice with.
   Main Menu:
   Use this to exit the current game and switch difficulty levels.
   

How to Order Fractions?
Ordering fractions is the process of arranging them from smallest to largest (least to greatest) or vice versa.

1. Fractions with the Same Denominator
   This is the easiest scenario. When the denominators (the bottom numbers) are the same, the “slices” are all the same size. You only need to look at the numerators (the top numbers).
   Rule:
   The larger the numerator, the larger the fraction.
   Example:
   Order \(\frac{2}{8}, \frac{5}{8}, and \frac{1}{8}\) from least to greatest.
   Result:
   \(\frac{1}{8} < \frac{2}{8} < \frac{5}{8}\)
   

2. Fractions with the Same Numerator
   This can be tricky. If the numerators are the same, it means you have the same number of pieces, but the size of the pieces is different.
   Rule:
   The smaller the denominator, the larger the fraction. This is because the whole is being divided into fewer (and therefore bigger) pieces.
   Example:
   Order \(\frac{1}{2}, \frac{1}{10}\), and \(\frac{1}{4}\) from least to greatest.
   Result:
   \(\frac{1}{10} < \frac{1}{4} < \frac{1}{2}\)
   

3. Fractions with Different Denominators
   When both numbers are different, you have three main strategies to compare them:
   A. Find a Common Denominator
   You can change the fractions so they all have the same bottom number.
   Find the Least Common Multiple (LCM) of the denominators.
   Convert each fraction to an equivalent fraction using that number.
   Compare the new numerators.
   Example: Compare \(\frac{2}{3}\) and \(\frac{3}{4}\).
   The LCM of 3 and 4 is 12.
   \(\frac{2}{3}\) becomes \(\frac{8}{12}\) (multiply top and bottom by 4).
   \(\frac{3}{4}\) becomes \(\frac{9}{12}\) (multiply top and bottom by 3).
   Result: Since 8 < 9, then \(\frac{2}{3} < \frac{3}{4}\).
   

B. Use Benchmark Fractions
Sometimes you don’t need math; you just need logic. Compare the fractions to 0, \(\frac{1}{2}\), or 1.
Example: Order \(\frac{1}{8}, \frac{4}{7}\), and \(\frac{11}{12}\).
\(\frac{1}{8}\) is very close to 0.
\(\frac{4}{7}\) is slightly more than \(\frac{1}{2}\) (since half of 7 is 3.5).
\(\frac{11}{12}\) is very close to 1.
Result: \(\frac{1}{8} < \frac{4}{7} < \frac{11}{12}\).

C. Cross multiplication is a “shortcut” method used to quickly determine which of two fractions is larger without having to find a full common denominator. It is often called the Butterfly Method because the loops you draw resemble butterfly wings.
To compare two fractions, such as \(\frac{2}{3}\) and \(\frac{3}{5}\):
Write the fractions side-by-side.
Multiply Diagonally (Bottom to Top):
Multiply the denominator of the second fraction by the numerator of the first fraction. Write the answer (the “product”) above the first fraction.
Multiply the denominator of the first fraction by the numerator of the second fraction. Write that product above the second fraction.
Compare the Products: The fraction with the larger product above it is the larger fraction.
This method only works for comparing two fractions at a time. If you have a list of four or five fractions to order, it is usually better to find a Least Common Denominator (LCD) for all of them. Or you can use benchmark fractions to sort some of the fractions and then use cross multiplication to sort the rest.

This video gives a clear, step-by-step approach to ordering fractions.

• Show Video

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.