Ordering Fractions

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.

<

and

<

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: 

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:

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.

Let's try to summarize what we have learned.

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: