Example 1: An 8ounce cup of milk was served to each of three children. Lisa drank 7 ounces of milk. Her sister Angie drank 3 ounces, and her brother Mark drank 5 ounces. What part of the cup did each child drink? Who drank the smallest part of the cup? Who drank the largest part of the cup? Who fell in the middle?
Analysis: Write the part of the cup that each child drank as a fraction, and then order them from least to greatest.
Child 
Milk Drank 
Fraction 
Lisa 
7 oz. 

Angie 
3 oz. 

Mark 
5 oz. 

Child 
Milk Drank 
Fraction 
Order 
Lisa 
7 oz. 


Angie 
3 oz. 


Mark 
5 oz. 


Solution: Angie drank the smallest part of the cup. Lisa drank the largest part of the cup. Mark fell in the middle.
We were able to order these fractions from least to greatest because they have like denominators.
To order fractions with like denominators, look at the numerators and compare them two at a time. It is helpful to write a number in a circle next to each fraction to compare them more easily.
Let's look at another example of ordering fractions with like denominators.
Example 2:
Solution:
Example 3: It takes Jack threefifths of an hour to complete his math homework, fivesixths of an hour to complete his reading homework, and twothirds of an hour to complete his science homework. Order the time spent to complete Jack's homework by subject from least to greatest.
Analysis: These fractions have unlike denominators. We will use the least common denominator (LCD) to write these fractions as equivalents fractions with like denominators, and then compare them two at a time.
Solution: Ordering the time spent on Jack's homework from least to greatest, we get: Math, Science and Reading.
To order fractions with unlike denominators, use the LCD to write them as equivalent fractions with like denominators. Then compare two fractions at a time. It is helpful to write a number in a circle next to each fraction to compare them more easily. Let's look at another example.
Example 4:

Analysis:


Solution: 
Example 5: Ned jogged for onethird of an mile, Moze jogged for onehalf of a mile, and Cookie jogged for onefifth of a mile. Order these distances from least to greatest.
Analysis:
Since these fractions have like numerators, we will compare the denominators two at a time. The fraction with the smaller denominator is the larger fraction.


Solution:

If you need a visual representation of example 5, look at the shaded rectangles below. These fractions are unit fractions: Each of them has the same numerator. You can see that as the denominator gets larger, the fraction gets smaller. 
To order fractions with like numerators, look at the denominators and compare them two at a time. The fraction with the smaller denominator is the larger fraction. Let's look at another example. 
Example 6: 



Solution: 

Example 7: 

Analysis: 
Convert these fractions to equivalent fractions with a common denominator. 


and 




Solution: 
Our answer is threeeighths. 
In example 7, we did not find the LCD. If we had, then it would be difficult to name a fraction between onefourth and twofourths. Instead, we chose eighths as our common denominator. This allowed us to name a fraction between twoeighths and foureighths, resulting in threeeighths as our answer. We could have also chosen larger common multiples of 2 and 4, such as 16, 24, 32, and so on. Since the number of common multiples of any two whole numbers is endless, there are many possible solutions to this problem. 
Let's try to summarize what we have learned.
R U L E S F O R O R D E R I N G F R A C T I O N S 
Relationship 
How To Order 
Like Denominators 
Compare two fractions at a time. Look at the numerators. The larger fraction is the one with the greater numerator. 
Unlike Denominators 
Convert each fraction to an equivalent fraction with a common denominator. Then compare two fractions at a time. The larger fraction is the one with the greater numerator. 
Like Numerators 
Compare two fractions at a time. Look at the denominators. The fraction with the smaller denominator is the larger fraction. 
Summary: When ordering three or more fractions from least to greatest, compare two fractions at a time. It is helpful to write a number in a circle next to each fraction to compare them more easily.
Exercises
In Exercises 1 through 5, click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. Note: To write the fraction twothirds, enter 2/3 into the form.
1. 
Order foursevenths, twosevenths and fivesevenths from least to greatest. Which is the least? 



2. 
Order twothirds, eightthirds and fivethirds from least to greatest. Which is the greatest? 



3. 
A chef takes threefourths of an hour to bake a pie, twothirds of an hour to bake cookies, and fivesixths of an hour to bake muffins. Which of these baked items had the shortest baking time? 



4. 
Maria jogged for twofifths of a mile, Laura jogged for onefourth of a mile, and Sasha jogged for threetenths of a mile. Who jogged the greatest distance? (Enter the name) 



5. 
Order fourthirds, foursevenths and fourfifths from least to greatest. Which is the least? 


