Ordering fractions involves arranging them from least to greatest or greatest to least. Here's a step-by-step guide on how to do it, based on the provided reference information:
Steps to Order Fractions
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Find the Lowest Common Multiple (LCM): Determine the LCM of the denominators of all the fractions you want to order. The LCM will be the new common denominator.
- For example, to order 1/2, 2/3, and 3/4, the LCM of 2, 3, and 4 is 12.
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Create Equivalent Fractions: Convert each fraction into an equivalent fraction with the LCM as the denominator. To do this, multiply both the numerator and denominator of each fraction by the number that makes the original denominator equal to the LCM.
- Continuing the example:
- 1/2 = (1 6) / (2 6) = 6/12
- 2/3 = (2 4) / (3 4) = 8/12
- 3/4 = (3 3) / (4 3) = 9/12
- Continuing the example:
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Compare the Equivalent Fractions: Once all fractions have the same denominator, compare their numerators. The fraction with the smallest numerator is the smallest fraction, and the fraction with the largest numerator is the largest fraction.
- In our example, comparing 6/12, 8/12, and 9/12, we see that 6 < 8 < 9.
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Write the Original Fractions in Order: Write the original fractions in the order determined by comparing the equivalent fractions. You can also express the order using inequality symbols (< or >).
- Therefore, the order from least to greatest is 1/2, 2/3, 3/4.
- Or, using inequality: 1/2 < 2/3 < 3/4
Example
Let’s order the fractions 2/5, 1/3, and 3/10.
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Find the LCM: The LCM of 5, 3, and 10 is 30.
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Create Equivalent Fractions:
- 2/5 = (2 6) / (5 6) = 12/30
- 1/3 = (1 10) / (3 10) = 10/30
- 3/10 = (3 3) / (10 3) = 9/30
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Compare the Equivalent Fractions: Comparing 12/30, 10/30, and 9/30, we find 9 < 10 < 12.
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Write the Original Fractions in Order: From least to greatest: 3/10, 1/3, 2/5.
- Or, using inequality: 3/10 < 1/3 < 2/5
