Order of Decimals, Mixed Numbers and Fractions

Ordering decimals, mixed numbers, and fractions together is a skill the GED Mathematical Reasoning test frequently assesses. When numbers appear in different forms, you must convert them to the same form before you can compare. The most reliable approach is to convert everything to a decimal, then arrange by value.

What Does It Mean to Order Decimals, Mixed Numbers, and Fractions?

To order a set of numbers means to arrange them from least to greatest (or greatest to least). When the numbers are in mixed forms — some as fractions, some as decimals, some as mixed numbers — the comparison is easiest if you first convert every number to the same format (typically a decimal) and then sort.

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How to Order Mixed Numbers, Fractions, and Decimals

Method 1: Convert all to decimals

Divide each fraction to get a decimal; bring down whole-number parts for mixed numbers. Then order the decimals.

• \(\color{blue}{\frac{3}{4} = 0.75}\)
• \(\color{blue}{0.5}\) stays as \(\color{blue}{0.5}\)
• \(\color{blue}{\frac{7}{8} = 0.875}\)
• \(\color{blue}{1.2}\) stays as \(\color{blue}{1.2}\)
• \(\color{blue}{\frac{5}{6} &\text{ approx }; 0.8&\#773;3}\)

Order: \(\color{blue}{0.5 < 0.75 < 0.8&\#773;3 < 0.875 < 1.2}\), so the original order from least to greatest is: \(\color{blue}{0.5, \frac{3}{4}, \frac{5}{6}, \frac{7}{8}, 1.2}\).

Method 2: Convert all to fractions with a common denominator

This works well when all values are fractions or easily written as fractions. Find the LCD and compare numerators.

• Compare \(\color{blue}{\frac{2}{3}}\) and \(\color{blue}{\frac{3}{5}}\): \(\color{blue}{\text{ LCD } = 15}\). \(\color{blue}{\frac{2}{3} = \frac{10}{15}}\), \(\color{blue}{\frac{3}{5} = \frac{9}{15}}\). So \(\color{blue}{\frac{3}{5} < \frac{2}{3}}\).

Step-by-Step Summary

1. Convert all numbers to decimals (divide fractions; write decimal parts for mixed numbers).
2. Align decimal points and compare digit by digit from left to right.
3. Arrange in the required order (least to greatest or greatest to least).
4. Rewrite the answer using the original form of each number.

Watch: Ordering Decimals, Fractions, and Mixed Numbers (Video Lesson)

This lesson walks through converting and ordering numbers in mixed forms:

Worked Examples

Example 1: Order from least to greatest: \(\color{blue}{\frac{7}{8}, 0.5, 1 \frac{1}{5}, \frac{3}{4}}\).

Convert: \(\color{blue}{\frac{7}{8} = 0.875}\), \(\color{blue}{0.5}\), \(\color{blue}{1 \frac{1}{5} = 1.2}\), \(\color{blue}{\frac{3}{4} = 0.75}\).
Order decimals: \(\color{blue}{0.5 < 0.75 < 0.875 < 1.2}\).
Answer: \(\color{blue}{0.5, \frac{3}{4}, \frac{7}{8}, 1 \frac{1}{5}}\).

Example 2: Order from greatest to least: \(\color{blue}{0.6, \frac{5}{8}, \frac{2}{3}}\).

Convert: \(\color{blue}{0.6}\), \(\color{blue}{\frac{5}{8} = 0.625}\), \(\color{blue}{\frac{2}{3} &\text{ approx }; 0.&\#773;6 = 0.6666\ldots}\)
Order: \(\color{blue}{0.6666\ldots > 0.6 > 0.625}\).
Answer: \(\color{blue}{\frac{2}{3}, 0.6, \frac{5}{8}}\).

Example 3: Order from least to greatest: \(\color{blue}{1 \frac{3}{4}, 1.5, 1 \frac{2}{3}}\).

All are between 1 and 2. Fractional parts: \(\color{blue}{\frac{3}{4} = 0.75}\), \(\color{blue}{0.5}\), \(\color{blue}{\frac{2}{3} &\text{ approx }; 0.667}\).
Order of fractional parts: \(\color{blue}{0.5 < 0.667 < 0.75}\).
Answer: \(\color{blue}{1.5, 1 \frac{2}{3}, 1 \frac{3}{4}}\).

Example 4: Which is greatest: \(\color{blue}{0.8}\), \(\color{blue}{\frac{4}{5}}\), or \(\color{blue}{\frac{7}{9}}\)?

Convert: \(\color{blue}{0.8}\), \(\color{blue}{\frac{4}{5} = 0.8}\), \(\color{blue}{\frac{7}{9} &\text{ approx }; 0.&\#773;7 = 0.777\ldots}\)
\(\color{blue}{0.8 = \frac{4}{5} > \frac{7}{9}}\). Answer: \(\color{blue}{0.8 \text{ and } \frac{4}{5} \text{ are tied } (\text{ equal }); \text{ both are greater than } \frac{7}{9}}\).

More Practice: Compare and Order Fractions and Decimals (Video)

This video teaches multiple methods for comparing and ordering fractions and decimals:

Exercises

Order each set from least to greatest.

1. \(\color{blue}{\frac{3}{5}, 0.7, \frac{1}{2}}\)
2. \(\color{blue}{1 \frac{1}{4}, 1.3, 1 \frac{1}{3}}\)
3. \(\color{blue}{0.25, \frac{1}{3}, \frac{3}{8}}\)
4. \(\color{blue}{2.5, 2 \frac{1}{4}, 2 \frac{3}{8}}\)
5. \(\color{blue}{\frac{5}{6}, 0.75, \frac{7}{8}}\)
6. \(\color{blue}{\frac{1}{2}, 0.4, \frac{2}{5}, 0.45}\)

Answers

1. \(\color{blue}{\frac{1}{2} (0.5) < \frac{3}{5} (0.6) < 0.7}\)
2. \(\color{blue}{1 \frac{1}{4} (1.25) < 1 \frac{1}{3} (1.&\#773;3) < 1.3}\) — Note: \(\color{blue}{1.3 > 1.&\#773;3 &\text{ approx }; 1.333}\)? No: \(\color{blue}{1.333 > 1.3}\). Corrected: \(\color{blue}{1 \frac{1}{4} < 1.3 < 1 \frac{1}{3}}\).
3. \(\color{blue}{0.25 < \frac{1}{3} (0.&\#773;3) < \frac{3}{8} (0.375)}\)
4. \(\color{blue}{2 \frac{1}{4} (2.25) < 2 \frac{3}{8} (2.375) < 2.5}\)
5. \(\color{blue}{0.75 < \frac{5}{6} (0.8&\#773;3) < \frac{7}{8} (0.875)}\)
6. \(\color{blue}{\frac{2}{5} (0.4) = 0.4 < 0.45 < \frac{1}{2} (0.5)}\)

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Frequently Asked Questions

What is the easiest way to compare fractions and decimals?

Convert all values to decimals first. This gives you a uniform format that is straightforward to compare digit by digit. Align the decimal points to avoid confusion.

How do I compare mixed numbers with different whole-number parts?

Compare the whole-number parts first. If they differ, the one with the larger whole number is greater. Only if the whole numbers are the same do you need to compare the fractional parts.

How does this appear on the GED test?

GED questions may ask you to arrange four or five numbers in order, choose the greatest or least value from a list, or place values on a number line. All of these require the same comparison strategy.

Related Topics

• Convert Between Fractions and Decimals
• Convert Between Decimals and Mixed Numbers
• Convert Between Improper Fractions and Mixed Numbers
• Simplifying Fractions
• Using Number Lines to Represent Integers