Least to Greatest Fractions Calculator

Q: How do you order 2/3, 3/5, and 7/10 from least to greatest?

3/5, 2/3, 7/10. The least common denominator is 30: 3/5 = 18/30, 2/3 = 20/30, 7/10 = 21/30. Numerator order 18 < 20 < 21 matches the decimals 0.6 < 0.666... < 0.7.

Q: Can I sort mixed numbers and decimals together?

Yes. The tool converts each entry to an exact fraction first. For example, with 2 1/2, 1 3/4, and 2.25: they become 5/2 = 2.5, 7/4 = 1.75, and 9/4 = 2.25, so the least-to-greatest order is 1 3/4, 2.25, 2 1/2.

Q: Can I sort fractions, decimals, and percents in one list?

Yes. With 50%, 1/3, and 0.4: 50% = 1/2 = 0.5, 1/3 = 0.333..., and 0.4 = 2/5. Using the common denominator 30 (10/30, 12/30, 15/30), the order from least to greatest is 1/3, 0.4, 50%.

Q: How do you compare two fractions with cross-multiplication?

To compare a/b and c/d, compare a times d with c times b. For example, 1/3 vs 1/2: 1x2 = 2 and 1x3 = 3; since 2 < 3, 1/3 < 1/2. This tool shows the cross-multiplication work for every neighboring pair in your sorted list.

Q: How do you order negative fractions?

The same way: convert to a common denominator or compare exact values. For -1/2, 1/4, -3/4 the order from least to greatest is -3/4, -1/2, 1/4. Remember that with negatives, the larger the absolute value, the smaller the number: -3/4 = -0.75 is less than -1/2 = -0.5.

Q: What does a repeating decimal like 0.333... mean?

It means the decimal never terminates: 1/3 = 0.333... goes on forever. This tool flags repeating decimals honestly instead of silently rounding them. Sorting still stays exact because comparisons use the underlying fractions (1/3), not the truncated decimal display.

Q: What is the common denominator method?

Find the least common multiple (LCM) of all denominators, rewrite each fraction with that denominator, then sort by the numerators. Example: for 1/2, 3/4, 1/3, the LCM of 2, 4, 3 is 12, giving 6/12, 9/12, 4/12 - so the order is 1/3, 1/2, 3/4. The result panel lists the LCD and each equivalent numerator.

Q: What if two entries are equal, like 2/4 and 1/2?

They are tied: both simplify to 1/2. The tool shows them as equal (2/4 = 1/2) and keeps your original input order for tied values, with their shared simplified form and decimal shown for each entry.

Q: Can I sort from greatest to least instead?

Yes. Enter your list and switch the order toggle to greatest-to-least. The same exact comparisons run; only the final display order is reversed.

Type a list of fractions, mixed numbers, decimals, or percents. This tool sorts them from least to greatest using exact fraction math, and shows the common denominator, decimal values, cross-multiplication steps, and a number line.

Your numbers (one per line, or separated by commas)

Accepted: fractions like 3/4, mixed numbers like 2 1/2, decimals like 0.75, percents like 75%, negatives like -1/2.

Type or paste your numbers above, then press Sort.

Number line

Worked examples

Example 1: basic fractions

Input: 1/2, 3/4, 1/3
Common denominator: 12 → 6/12, 9/12, 4/12
Order: 1/3, 1/2, 3/4 (decimals: 0.333..., 0.5, 0.75)

Example 2: close values

Input: 2/3, 3/5, 7/10
Common denominator: 30 → 20/30, 18/30, 21/30
Order: 3/5, 2/3, 7/10 (decimals: 0.6, 0.666..., 0.7)

Example 3: mixed numbers and decimals

Input: 2 1/2, 1 3/4, 2.25
As fractions: 5/2, 7/4, 9/4; common denominator 4
Order: 1 3/4, 2.25, 2 1/2 (decimals: 1.75, 2.25, 2.5)

Example 4: fractions, decimals, percents

Input: 50%, 1/3, 0.4
As fractions: 1/2, 1/3, 2/5; common denominator 30 → 15/30, 10/30, 12/30
Order: 1/3, 0.4, 50% (decimals: 0.333..., 0.4, 0.5)

How it works

Parse: each entry becomes an exact fraction. 2 1/2 becomes 5/2, 0.75 becomes 3/4, 75% becomes 3/4.
Common denominator: the tool computes the least common multiple of all denominators and rewrites every value over it.
Sort: numerators are compared with exact integer cross-multiplication. No floating-point numbers are used, so repeating decimals like 1/3 can never be mis-sorted by rounding.
Explain: you get decimal values (repeating ones flagged honestly), the cross-multiplication for every neighboring pair, and a number line.

What you can do here: order fractions from least to greatest, arrange fractions in ascending order, sort mixed numbers from least to greatest, order fractions, decimals, and percents in one list, or flip the toggle to sort from greatest to least. Three ways of ordering fractions with different denominators are shown: the common denominator, exact decimal values, and cross-multiplication. Use the worked examples to check your worksheet answers.

Which tool do you need?

This tool orders a list of values from least to greatest.
Fraction to Percent Calculator: converts one fraction to a percent.
Fraction to Decimal Calculator: converts one fraction to a decimal.
Percent Difference Calculator: compares exactly two numbers.

Frequently asked questions

How do you order fractions from least to greatest?

Convert every value to the same form, then compare. This tool does it two ways at once: (1) it finds a common denominator (the least common multiple of all denominators) and compares the numerators, and (2) it computes each exact decimal value. Because all the math is done with exact fractions instead of floating-point, the order is always correct, even for repeating decimals like 1/3 = 0.333...

What is the order of 1/2, 3/4, and 1/3 from least to greatest?

1/3, 1/2, 3/4. The common denominator is 12: 1/3 = 4/12, 1/2 = 6/12, 3/4 = 9/12. Comparing numerators 4 < 6 < 9 gives the same order as the decimals 0.333... < 0.5 < 0.75.

How do you order 2/3, 3/5, and 7/10 from least to greatest?

3/5, 2/3, 7/10. The least common denominator is 30: 3/5 = 18/30, 2/3 = 20/30, 7/10 = 21/30. Numerator order 18 < 20 < 21 matches the decimals 0.6 < 0.666... < 0.7.

Can I sort mixed numbers and decimals together?

Yes. The tool converts each entry to an exact fraction first. For example, with 2 1/2, 1 3/4, and 2.25: they become 5/2 = 2.5, 7/4 = 1.75, and 9/4 = 2.25, so the least-to-greatest order is 1 3/4, 2.25, 2 1/2.

Can I sort fractions, decimals, and percents in one list?

Yes. With 50%, 1/3, and 0.4: 50% = 1/2 = 0.5, 1/3 = 0.333..., and 0.4 = 2/5. Using the common denominator 30 (10/30, 12/30, 15/30), the order from least to greatest is 1/3, 0.4, 50%.

How do you compare two fractions with cross-multiplication?

To compare a/b and c/d, compare a times d with c times b. For example, 1/3 vs 1/2: 1x2 = 2 and 1x3 = 3; since 2 < 3, 1/3 < 1/2. This tool shows the cross-multiplication work for every neighboring pair in your sorted list.

How do you order negative fractions?

The same way: convert to a common denominator or compare exact values. For -1/2, 1/4, -3/4 the order from least to greatest is -3/4, -1/2, 1/4. Remember that with negatives, the larger the absolute value, the smaller the number: -3/4 = -0.75 is less than -1/2 = -0.5.

What does a repeating decimal like 0.333... mean?

It means the decimal never terminates: 1/3 = 0.333... goes on forever. This tool flags repeating decimals honestly instead of silently rounding them. Sorting still stays exact because comparisons use the underlying fractions (1/3), not the truncated decimal display.

What is the common denominator method?

Find the least common multiple (LCM) of all denominators, rewrite each fraction with that denominator, then sort by the numerators. Example: for 1/2, 3/4, 1/3, the LCM of 2, 4, 3 is 12, giving 6/12, 9/12, 4/12 - so the order is 1/3, 1/2, 3/4. The result panel lists the LCD and each equivalent numerator.

What if two entries are equal, like 2/4 and 1/2?

They are tied: both simplify to 1/2. The tool shows them as equal (2/4 = 1/2) and keeps your original input order for tied values, with their shared simplified form and decimal shown for each entry.

Can I sort from greatest to least instead?

Yes. Enter your list and switch the order toggle to greatest-to-least. The same exact comparisons run; only the final display order is reversed.

Why is a fraction with denominator 0 an error?

Division by zero is undefined - 5/0 has no value at all, so it cannot be placed in any order. The tool flags it honestly instead of guessing. Change the denominator to any non-zero number to include it.

How many numbers can I sort at once?

As many as you can type: one per line or separated by commas. Each entry can be a fraction (3/4), a mixed number (2 1/2), a decimal (0.75), or a percent (75%). The common denominator grows with the LCM of all denominators, which can get large with many entries - that is shown so you can judge the arithmetic.

Is the sorting exact or rounded?

Exact. Every value is stored as an exact fraction (numerator/denominator) and every comparison is done by cross-multiplication with integer arithmetic - no floating-point numbers are used in the sort. Rounding only ever appears in the displayed decimal text, which is clearly marked when it repeats.

Free tool by NRTechStudio

Least to Greatest Fractions Calculator

Example 1: basic fractions

Example 2: close values

Example 3: mixed numbers and decimals

Example 4: fractions, decimals, percents

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