Fractions are a vital part of mathematics and understanding them is very important and crucial in everyday life. From dividing a pizza among friends to measuring ingredients in a recipe, fractions make our lives easier. But what happens when we need to compare or arrange them? That’s where ordering fractions comes in.

Before dividing into the concept of ordering fractions, it is essential to apprehend the basics of fractions. A fraction present a part of a whole or a set of a number (value). There are two parts of a fraction, one is numerator (upper part) which specifies the share of the whole and second one is denominator (bottom part) which denotes all parts of the number.

In this blog, we’ll explain the concept of ordering fractions, the methods used to order them and give some useful examples to make it easier to understand.

## What is Ordering Fraction?

Ordering fractions is the process of arranging fractions from lowest to highest or vice versa. It’s an important skill that is used in many math problems and real-life situations. When ordering fractions, we use the inequality symbols (<, >, =) to compare fractions and determine their relative positions. Basically, fractions are of three categories.

- First one category is proper fraction in which numerator (upper part of the number) is less than bottom part of the number (denominator).
- Second one improper fraction in which upper part of the number (numerator) is greater than that of bottom part (denominator).
- Third and last one is mixed fraction also termed as co-fraction in which mixed number combine an integer and a proper fraction.

It is an essential to know how to convert mixed numbers too improper fractions, which is done by multiplying the denominator by the integer and adding the numerator.

## Methods Used for Ordering Fractions:

Here in the following we will elaborate some useful methods which are commonly used for the ordering of fractions.

- Using common denominators
- Using Decimal or Percentage Conversion
- Using Cross Multiplication
- Using Simplification of Fractions

### Using Common Denominators:

In this method, ordering of fractions is carried out by computing a common denominator (Least common multiple) for the fractions under observation. Afterwards its an easy task to arrange fractions in ascending or descending order on the basis of their numerator’s comparison. In this method, mainly three steps are to follow for ordering of fractions.

Step 1: Compute L.C.M of all given fraction’s denominators. It will be considered denominator for all the fractions.

Step 2: Convert each fraction to an equivalent fraction with the common denominators.

Step 3: Arrange the fractions based on the value of their numerators.

### Using Decimal / Percentage Conversion:

Sometimes it is difficult to find common denominator for all the given fractions due to their complexity. So to avoid that sort of complexity each fraction is converted into its decimal form or we compute its percentage in order to compare them. By comparing their percentage or decimals, fractions can be ordered in the required form ascending or descending order form. In this method, basically two steps are to follow for ordering of fractions.

Step 1: Convert all the given fractions into their decimal form or compute the percentage for all of them.

Step 2: Compare these obtained values for the required ordering of the fractions.

### Using Cross Multiplication:

In this method, cross multiplication of fractions is carried out i.e. numerators and denominators of alternate fractions are multiplied with one another. Then obtaining result of cross multiplication we compare the resulted products. Once results are obtained, we compare the resulted products for ordering of the given fractions.

### Using Simplification of Fractions:

In this method, we simplify the given fractions at first and then we order the given fractions as ascending or descending order of size. On simplification of fractions, its an easy task to order the given fraction in ascending or descending order. In this method we point out the lowest terms and then simplify the given fractions up to practicable but entirely depends on the fractions involved.

## How to order the fractions?

You can use a greatest to least calculator to order the fractions in ascending or descending manners without any difficulty. Here are a few examples to order fractions manually.

**Example 1:**

Order the following fractions in form of their size.

1/6, 2/3, 5/12, 1/4

**Solution: **

**Step 1:** Given data

1/6, 2/3, 5/12, 1/4

**Step 2:** Compute LCM of the denominators (3,4,6,12) of all the given fractions which is 12. So, we can convert the fractions having same denominators by multiplying with suitable number as

1/6 x 2/2 = 2/12

2/3 x 4/4 = 8/12

5/12 x 1/1 = 5/12

1/4 x 3/3 = 3/12

**Step 3:** Point out the smallest fraction observing the numerators and order the fractions.

2/12, 3/12, 5/12, 8/12

So, the fractions in order of size form as they are appeared in question.

1/6, 1/4, 5/12, 2/3 (Fractions are in ascending order which is the required result).

**Example 2: **

Order the following fractions in form of their size.

5/3, 1 1/2, 1 3/6, 25/18

Solution:

**Step 1:** Given data

5/3, 1 1/2, 1 1/6, 25/18

**Step 2:** Here we can write mixed fractions as improper fractions or improper fractions as a mixed one. But it is an easy task to write all fractions in mixed form and focus on the fractional part of these mixed fractions.

5/3 = 1 2/3

25/18 = 1 7/18

**Step 3:** Now we compute the LCM of the denominators (2, 3, 6, 18) of all the given fractions which is 18. So, we can convert the given fractions having same denominators by multiplying with a suitable number.

5/3 = 1 2/3 = 1 2×6/3×6 = 1 12/18

1 1/2 = 1 1×9/2×9 = 1 9/18

1 1/6 = 1 1×3/6×3 = 1 3/18

25/18 = 1 7×1/18×1 = 1 7/18

**Step 4:** Point out the smallest fraction observing the numerators of the above given mixed fractions and ordering the fractions in order of size.

1 3/18, 1 7/18, 1 9/18, 1 12/18

So, the fractions in order of size in the form as they are appeared in question.

1 1/6, 25/18, 1 1/2, 5/3 (Fractions are in ascending order which is the required result).

# Conclusion:

Ordering fractions is a fundamental skill in math and everyday life. Understanding fractions’ basics and the two commonly used methods of ordering fractions can make the process easier. With practice, anyone can master the skill and use it to solve complex math problems and real-life situations without difficulty.

**Correct Answer: **Example 1: ✔

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