How to put fractions in order from least to greatest with different denominators

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.

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Child	Milk Drank	Fraction	Order
Lisa	7 oz.
Angie	3 oz.
Mark	5 oz.

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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: 

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 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.

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.

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.

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?

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

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?

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)

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