A fraction is a number that represents the part of a whole or any other defined quantity. It comprises two integers separated by a vinculum (bar), where the integer on top of the bar is the numerator, and the integer on the bottom is the denominator. Ordering fractions involves arranging them from least to greatest (ascending order) or greatest to least (descending order).

Ordering fraction play a vital role in mathematics and our daily lives to compare and rank any fractional quantities. In this article, we will examine the concept of ordering fractions and learn how to order the fractions from least to greatest and greatest to least through multiple examples.

The order of fractions refers to the arrangement of fractions according to their sizes. This sequence can be either ascending (smallest to largest) or descending (largest to smallest).After writing in clear order, identifying the larger and smaller fractions becomes easier.

Consider a real-world example to understand this concept clearly. Sophia plans to divide a pizza into 8 equal slices to share among her friends. She wants one-fourth of the pizza for herself, while John is asking for one-eighth, and Sarah is requesting four-eighth. Ordering these fractions is essential to determine who got the largest and smallest slices.

Here are two different methods that can be used to order the fractions in ascending or deseeding order.

- By Using Common Denominator
- By Converting fractionsto Decimal form

To order the fraction by using the common denominator method, follow these steps:

- Find the least common multiple (LCM) of denominators of the given fractions.
- Multiply the numerator and denominatorby thesuitable factor to ensure all fractions share the same least common denominator (LCD).
- Now, fractionshave the same denominator so compare their numerator and arrange them from least to greatest or greatest to least.

Let’s take an example for a clear understanding of the above steps.

**Example: Order the fractions 1/2, 2/3, and 3/5 from greatest to least.**

**Step 1: **Find the LCM of 2, 3 and 5.

L.C.M = 30

**Step 2:** Multiply the numerator and denominator of each fraction by the appropriate factors.

1/2 = (1/2) × (15/15) = 15/30

2/3 = (2/3) × (10/10) = 20/30

3/5 = (3/5) × (6/6) = 18/30

**Step 3:**Compare the numerator of the obtained fractions and order them in descending order.

20/30, 18/30, 15/30

Replace the equivalence fractions with their corresponding original fractions.

2/3, 3/5, 1/2

That is in the required order of the given fractions.

Here are some easy steps to order the fractions in the desired arrangement by division method.

- Divide the top number (numerator) by the bottom number (denominator) for each fraction to get their decimal form.
- Start by looking at the whole number part of the decimals. If one decimal has a larger whole number part than another, it is automatically larger.
- If the whole parts are the same, move to the decimal part. Compare the tenths, hundredths, thousandths, and so on, in the decimals. The decimal with the larger digit in that position is the larger number.
- Arrange the decimal number by comparing the whole part and digit by digit from left to right after the decimal point.
- Finally, replace the decimal numbers with their corresponding fractions.

Consider an example to understand the above steps practically.

**Example: Order the fractions 3/5, 2/7, and 4/5 from least to greatest.**

**Step 1:** Convert the given fractions to decimal form.

3/5= 0.600

2/7= 0.286

4/5= 0.800

**Step 2:**Compare the whole parts of the above decimal numbers. The decimals have the same whole number part (0), so move to the digits after the decimal point.

**Step 3:**Compare the digits from left to right after the decimal points and arrange from least to greatest.

0.286, 0.600, 0.800

Replace the decimal numbers with their corresponding fractions.

2/7, 3/5, 4/5

That is the least to greatest order of the given fractions.

You can also use online ordering fractions calculators to order from least to greatest and vice versa with steps according to the methods of ordering fractions.

- Make ensure all fractions have the same denominator before comparing them.
- If the denominators are the same in each fraction, compare their numerators directly.
- If the fractions have different denominators, convert all fractions to equivalent fractions with the common denominator.
- Regularly practice ordering fractions to become more proficient in it.

**Example: **

Sarah runs for 3/8 of an hour on Monday, 1/4 of an hour on Tuesday, and 5/6 of an hour on Wednesday. Order the time spent running each day from least to greatest.

**Solution:**

8, 4, 6 | |

2 | 4, 2, 3 |

2 | 2, 1, 3 |

3 | 1, 1, 3 |

1, 1, 1 |

**Step 1: **Calculate the least common multiple of the denominator of the given fractions.

L.C.M of 8, 4, and 6 = 2 × 2 × 2 × 3 =24

**Step 2:**Multiply the numerator and denominator of each fraction by the suitable factors.

**Step 3: **Compare the numerator of the resulting fractions and order them from least to greatest.

1/4, 3/8, 5/6

Thus, the time spent running each day from least to greatest:

Tuesday, Monday, and Wednesday.

**Example: **

Tom divided a cake among his friends, giving 3/7 of the cake to Alex, 4/9 to the Maria, and 5/6 to the Isabella. Order the fraction of the cake each friend received from greatest to least.

**Solution: **

**Step 1:**Convert the given fractions to decimal form.

**Step 2: **Compare the whole parts of the above decimal numbers. The decimals have the same whole number part (0), so move to the digits after the decimal point.

**Step 3: **Compare the digits from left to right after the decimal points and arrange from greatest to least.

0.833, 0.444, 0.429

Replace the decimal numbers with their corresponding fractions.

5/6, 4/7, 3/7

Therefore, the fractions are in order from greatest to least: Isabella, Maria, Alex.

In this article, we have learned about ordering fractions, which is the process of arranging fractions in either ascending (smallest to largest) or descending (largest to smallest) order. We have also explored the steps on how to order the fractions and covered many examples for better understanding.

**Also Read: A-Level Choices: 5 Tips to Help Your Child Make the Right Decision**