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Ordering Fractions Unit 14 > Lesson 6 of 11


Example 1: An 8-ounce 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.
< and <
< <
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: 
Fraction Order
Solution:

Example 3:  It takes Jack three-fifths of an hour to complete his math homework, five-sixths of an hour to complete his reading homework, and two-thirds 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.
Math:
Reading:
Science:
Math:
Reading:
Science:

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 one-third of an mile, Moze jogged for one-half of a mile, and Cookie jogged for one-fifth 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.
Fraction Order
< and <
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: 
Fraction Order
Solution:

Example 7: 
Analysis: Convert these fractions to equivalent fractions with a common denominator.
and
< <
Solution: Our answer is three-eighths.


In example 7, we did not find the LCD. If we had, then it would be difficult to name a fraction between one-fourth and two-fourths. Instead, we chose eighths as our common denominator. This allowed us to name a fraction between two-eighths and four-eighths, resulting in three-eighths 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 two-thirds, enter 2/3 into the form.

1.  Order four-sevenths, two-sevenths and five-sevenths from least to greatest. Which is the least?
ANSWER BOX:

RESULTS BOX:


2.  Order two-thirds, eight-thirds and five-thirds from least to greatest. Which is the greatest?
ANSWER BOX:

RESULTS BOX:


3.  A chef takes three-fourths of an hour to bake a pie, two-thirds of an hour to bake cookies, and five-sixths of an hour to bake muffins. Which of these baked items had the shortest baking time?
ANSWER BOX:

RESULTS BOX:


4.  Maria jogged for two-fifths of a mile, Laura jogged for one-fourth of a mile, and Sasha jogged for three-tenths of a mile. Who jogged the greatest distance? (Enter the name)
ANSWER BOX:

RESULTS BOX:


5.  Order four-thirds, four-sevenths and four-fifths from least to greatest. Which is the least?
ANSWER BOX:

RESULTS BOX:



This lesson is by Gisele Glosser. You can find me on Google.

Lessons on Fractions
Introduction to Fractions
Classifying Fractions
Equivalent Fractions
Simplifying Fractions
Comparing Fractions
Ordering Fractions
Converting Fractions to Mixed Numbers
Converting Mixed Numbers to Fractions
Practice Exercises
Challenge Exercises
Solutions

Related Activities
Interactive Puzzles
Printable Worksheets
Fraction Goodies Game

Need More Practice?
Try our Fractions Worksheet Generator


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