Rearrange Fractions

About rearranging fractions

Enter multiple integers, decimals, or fractions and click the "Rearranges" button to convert the entered fractions to equivalent fractions with a common denominator and display the result.

By changing "Sort by", you can sort by "Ascending order (high number from small number)" or "Descending order (small number from high number)".

You can enter integers, decimals, and fractions.

For fractions, separate them with a "/" symbol, and for mixed fractions, write the integer part, leave a space, and then write the fraction.

The calculation method is also displayed along with the calculation.

How to rearrange fractions

To rearrange fractions, you first need to convert each number so that they can be compared.

When it comes to fractions with different denominators, it's not easy to compare their sizes, so the first method is to make the denominators of the fractions the same.

Alternatively, you can convert all of the fractions into decimals so that they are easier to compare and sort by.

How to align the denominators of fractions

  • 1. To make the denominators the same, first calculate the least common multiple of the denominators.
  • 2. Multiply the numerator and denominator by the same value so that the denominator of each fraction becomes the value found in step 2.
  • 3. Since the denominators are the same, we rearrange them by comparing the size of the numerators.

Example: Sort 34, 47, 58 in ascending order.

To make the denominators the same, first calculate the least common multiple of the denominators.

The least common multiple of 4, 7, and 8 is 56.

Multiply each fraction by 14, 8, and 7 so that the denominator is 56.

34, 47, 58

= 3 × 144 × 14 , 4 × 87 × 8 , 5 × 78 × 7

= 4256 , 3256 , 3556

Therefore, converting 34, 47, 58 to an equivalent fraction with a common denominator gives us 4256, 3256, 3556.

If we rearrange this from smallest numerator to largest numerator, we get 3256 < 3556 < 4256, so if we rearrange the original fraction in ascending order, we get 47 < 58 < 34.

How to convert a fraction to a decimal

  • 1. To convert a fraction to a decimal, it can be calculated by dividing the numerator by the denominator.
  • 2. For mixed fractions, you can add the integer parts separately and calculate the fraction as integer part + (numerator ÷ denominator).
  • 3. Convert everything to decimals and then compare the magnitudes.

Example: Sort 76, 89, 113 in ascending order.

Convert to a decimal by dividing the numerator by the denominator.

7 ÷ 6 = 1.1666...

8 ÷ 9 = 0.8888...

For mixed fractions, add the integer parts separately and calculate as integer part + (numerator ÷ denominator).

1 + (1 ÷ 3) = 1.3333...

If you sort this from smallest to largest, you get 0.8888... < 1.1666... < 1.3333..., so if you sort the original fraction in ascending order, you get 89 < 76 < 113.

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