Our Least to greatest calculator orders all types of numbers (non-fraction numbers, fraction numbers, mixed numbers, and decimal numbers) from least to greatest as well as greatest to least order.

This ordering fractions calculator arranged the numbers by using two different methods: converting fractions to decimals and fractions to common denominators to find the LCD of inputs.

## What is least to greatest?

It is the arrangement of the number in ascending order (from smaller to larger number). This arrangement is done for all types of numbers whether these are fractions, improper fractions, non-fractions, or decimal numbers.

The arrangement of non-fraction numbers is easy, simply identify the smaller number and arrange the number from smaller to larger. However, for the arrangement of fractions numbers, adopt special methods. Below we discuss these methods in complete detail.

When writing a simple number in the least to greatest order, then write the smallest number on the left, with the next smallest number that is written to its right, and carry on for the last largest number.

For example: If the numbers are “**2, 5, 8, 1, **and** 3**” then in least to greatest order is written as “**1, 2, 3, 5, **and** 8**” or **1 **< **2 **< **3 **< **5 **< **8**.

## How to order fractions?

For the simple non-fraction number is easy to decide which number is small or large. However, for the non-fraction number is quite difficult to decide which is smaller or greater by simply seeing the numerator and denominator values.

To identify which fraction is greater or smaller adopt some special methods. These methods are discussed below.

There are five different methods to order any fractions.

- Converting fractions to decimals
- Convert to Common Denominator (by finding LCD)
- Cross-Multiplication Method
- Visualization of fractions Using Number Lines
- Use of Benchmarks (like 0, 1/2, and 1)

Here we discuss the first two most common methods, which are used to order the group of fraction numbers in ascending or descending order. Also, we will provide detailed manual examples to order the fractions with these methods.

### 1. Converting Fractions to Decimals

In this method, convert all fraction numbers into decimals then arrange them into least to greatest order by comparing the decimal value of the fraction numbers.

Use this sign “<” for ascending order and write the least value fraction first, then write the second smallest value fraction, and move up to the largest value of the fraction to arrange all fractions.

To clear this method see the below manual example. Also, use our above Least to greatest calculator that orders any group of fractions in the least to greatest order.

**Example**:

Arrange the given fractions numbers “12/30, 5/6, 8/24, 8/9, and 6/7” from least to greatest order by converting fractions to decimal.

**Solution:**

**Step 1**: First, divide each fraction by the denominator and find the decimal value.

Fraction | Decimal |
---|---|

12/30 | 0.400 |

5/6 | 0.833 |

8/24 | 0.333 |

8/9 | 0.889 |

6/7 | 0.857 |

**Step 2**: Analyze all values and arrange them in ascending order.

Decimal | Fraction |
---|---|

0.33 | 8/24 |

0.400 | 12/30 |

0.833 | 5/6 |

0.857 | 6/7 |

0.889 | 8/9 |

**Thus, **the final order fraction from least to greatest is “**8/24 **<** 12/30 **<** 5/6 **< **6/7 **<** 8/9**”.

** Note**: To write the above fraction in the greatest to least (descending) order just write from right to left with this sign “

**>**”. i.e.,

**8/9**>

**6/7**>

**5/6**>

**12/30**>

**8/24**.

### 2. Convert to Common Denominator

In this method, arrange fractions by making the same denominator for all fractions to find the least common denominator (LCD). After converting all fractions with the same denominator, then compare their numerators. To find the LCD of fractions use an LCD calculator.

Moreover, to arrange in the least to greatest order use the sign “**<**” between the fractions. Write the least numerator value fraction first, then write the second smallest numerator value fraction, and move up to the largest numerator value of the fraction.

See the below example to understand, how to make the same denominator of each fraction.

**Example:** Arrange given fraction numbers “**4/3, 7/5, 8/7, 3/2, **and **5/4**” in ascending order by making the Common Denominator.

**Solution:**

**Step 1: **Note all fractions and also their numerator & denominator.

Fraction = 4/3, 7/5, 8/7, 3/2, 5/4

Numerator = {4, 7, 8, 3, 5}

Denominators = {3, 5, 7, 2, 4}

**Step 2**: Find the least common denominator of all fractions.

To find the LCD value, find the factors of all denominator values or simply find the LCM of all values. To find LCM use the LCM calculator.

Now we find the factors manually:

**3 **= 3

**5 **= 5

**7 **= 7

**2 **= 2

**4** = 2^{2}

LCD (3, 5, 7, 2, 4) = 2^{2} x 3 x 5 x 7 = **420**

**LCD **=** 420**

**Step 3**: Multiply & divide by the LCD with each fraction and simplify the fraction to make the same denominator.

**4/3** = (4/3) × (420/420) = 560/420

**7/5** = (7/5) × (420/420) = 588/420

**8/7** = (8/7) × (420/420) = 480/420

**3/2** = (3/2) × (420/420) = 630/420

**5/4** = (5/4) × (420/420) = 525/420

**Step 4**: Now, compare the numerator and arrange it in the least to greatest order.

Numerator | Fraction |
---|---|

480 | 8/7 |

525 | 5/4 |

560 | 4/3 |

588 | 7/5 |

630 | 3/2 |

**Thus, **the final order fraction in the least to greatest is “**8/7 **<** 5/4 **<** 4/3 **< **7/5 **<** 3/2**”.

** Note**: To arrange the above result in descending order, simply write the above ascending order from right to left with the sign “

**>**”. i.e.,

**3/2**>

**7/5**>

**4/3**>

**5/4**>

**8/7**.

To verify the above result use our above ordering fraction calculator which arranges the fractions from least to greatest (greatest to least) order.

## Frequently Ask Question's (FAQ’s)

**How to order numbers from least to greatest?**

To order any numbers from least to greatest (ascending order), follow these steps:

**For Whole Numbers**: Arrange them from the smallest to the largest.**For Decimals**: Compare each number from the leftmost digit to the right, arranging them in increasing order.**For Fractions**: Convert them to decimals or find a common denominator, then compare and order them.**For Mixed Numbers**: Convert all numbers to a common form (e.g., decimals) for easy comparison, then arrange from smallest to largest.

Alternatively, use the above least to greatest calculator to simplify this process and get accurate results quickly.

**What is ascending and descending order?**

Ascending order is a technique to arrange numbers from smallest to largest, with the smallest number first and the largest number last. However, descending order is the opposite technique of arranging numbers from largest to smallest.

**How, this calculator is helpful for educational purposes?**

Our online calculator is an excellent tool for students and educators. It provides step-by-step explanations, making it useful in learning how to order numbers. Also, understand mathematical concepts to arrange fractions, non-fractions, mixed fractions, and decimals numbers using two common methods.

**What is the difference b/w making the same denominator and converting fractions to decimals methods?**

The **LCD method** finds a common denominator of all fractions and then compares their numerators. The **decimal conversion method** converts all fractions into decimal form and then compares the values to arrange the fractions. Both methods give the same result, but the decimal method is quicker to arrange any fraction numbers.

**Can this calculator handle the negative numbers**** & improper fractions?**

Yes, our ascending order calculator can handle negative numbers, proper, and improper (mixed) fractions. It converts them into comparable formats and arranges them in the correct order to ascending (descending).