Ordering fraction is a fundamental mathematical concept used to arrange fractions in ascending or descending order, from least to greatest and greatest to least. The skill is very crucial in mathematics and statistics, as it helps us to find the correct arrangements of numbers to solve algebraic and central tendency problems.

In this article, we’ll understand the definition, explore the techniques, methods and try to understand the concept of ordering fraction with examples.

## What is an ordering fraction?

The ordering fraction is a basic concept used to ordered the fraction in such order that it can be ascending or descending, from increasing to decreasing, from least to greatest and greatest to least, from smaller to larger and larger to smaller.

We can rearrange all types of fractions it can be proper fractions, improper fractions and mixed fractions.

Proper Fraction | Improper Fraction | Mixed Fraction |

A fraction where the numerator is less than the denominator 3/4 | A fraction where the numerator greater than the denominator 5/2 | A number that is made up of a whole number plus a fraction 9 2/5 |

## Methods of ordering fractions:

There are two common techniques of ordering the fractions are as follows:

- By taking common denominator by using the technique of LCM in all fractions.
- By changing the fractions into decimal and then ordering it.

### Common denominator in all fractions:

In this technique we have to make the common denominator in all the fraction then we’ll be able to rearrange it by comparing the numerator of that fraction. For this purpose, we have to multiply and divide the same number with numerator or denominator of that fraction.

When we get a same denominator in different fraction then the next step is to compare the numerator of all the fraction. By comparing the numerator of different fractions, we would be able differentiate that which fraction is smaller or which is larger in this way we can easily arranged the fractions in ascending or descending orders.

Some fractions which having different numerator and denominator are as follows:

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

First of all, we have to made the value of denominator same in all above fractions. For this, we have to multiply and divide the numerator and denominator of above fraction with the same number.

Like,

1/2 | x | 6/6 | = | 6/12 |

2/3 | x | 4/4 | = | 8/12 |

5/6 | x | 2/2 | = | 10/12 |

1/12 | x | 1/1 | = | 1/12 |

Now, we can see after multiplying or dividing with the same number in the above fraction we get the same denominator.

The next step is to comparing the numerator of that fractions which we get after the multiplication or division. So, in this way we can easily rearrange the fraction from larger to smaller order, also in ascending or descending order.

Where the value numerator would be greater than the fraction would also be greater from the other fractions.

Like,

In the above fractions, the ‘10’ is the numerator which is greater than other numerators so this fraction is greater than the other fractions. We can write it in descending order like this,

10/12, 8/12, 6/12, 1/12

In simple form of fraction,

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

We also can write it in ascending order which would be like this,

1/12, 6/12, 8/12, 10/12

In simple form of fraction,

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

This is the method or technique of ordering fractions by making the common denominator and then comparing the numerator of all the fractions. In simple words, we can say that this is the technique of making the denominator same in all fractions.

### By converting the fraction into decimal form:

The technique of converting fraction into decimal is another way of ordering the fractions. This is the easiest way or technique of arranging fraction in the ascending or descending order.

In this technique, first of all we have to divide the numerator of the fraction with denominator of the fraction and get the decimal form of that fraction then we’ll these decimals. In this way, we would be able to differentiate that which one fraction is greater or which one is smaller.

And in this way, we can easily rearrange these fractions in ascending or descending order.

For example, we are going to rearrange the numbers in descending order or ascending order but we don’t know that which fraction is greater or which one is smaller. So, we use this technique.

Fraction | Decimal |

1/2 | 0.5 |

2/3 | 0.67 |

5/6 | 0.84 |

1/12 | 0.08 |

Now, we can easily differentiate that which fraction is greater or which one is small by using their decimal form and we can easily rearrange them in the order of greatest to smallest.

## Examples of ordering fractions

Some examples are as follows:

**Example 1:**

Order the following fractions from smaller to greater by using the LCM method or technique.

3/2, 1 1/4, 1 1/8, 13/12.

**Solution:**

**Step 1:** First of all, we have to convert all the simple fractions into mixed fractions.

3/2 = 1 1/4

13/12 = 1 1/12

**Step 2:** Now, by using the LCM method the common factor is 24.

1 1×12/2×12 = 1 12/24

1 1×6/4×6 = 1 6/24

1 3×3/8×3 = 1 9/24

1 1×2/12×2 = 1 2/24

**Step 3:** By comparing the numerator of all mixed fractions which had the same denominator.

1 2/24, 1 6/24, 1 9/24, 1 12/24

So, we can clearly see that the numerator ‘2’ is smaller and ‘12’ is larger. We rearrange the mixed fractions according to the condition from smaller to larger order.

**Step 4:** By using the above comparison of mixed we can rearrange the simple and mixed both fractions which are mentioned in question.

13/12, 1 1/4, 1 3/8, 3/2

This is the required answer of the given question.

The arrangement of fractions in ascending or descending orders can be done easily with the help of online ordering fraction calculators.

**Example 2:**

Rearrange these fractions into descending order by using the decimal technique.

5/2, 1/3, 4/3, 11/10, 8/5, 5/8, 7/9, 1/2

**Solution:**

**Step 1:** First of all, we have converted all the above fractions into decimal form.

5/2 = 2.5

1/3 = 0.33

4/3 = 1.33

11/10 = 1.1

8/5 = 1.6

5/8 = 0.625

7/9 = 0.78

1/2 = 0.5

**Step 2:** In this step, we have to rearrange the fractions according the order mention in question by using the decimals.

Firstly, we rearrange the decimals values in descending order.

2.5, 1.6, 1.33, 1.1, 0.78, 0.625, 0.5, 0.33

Now, by seeing this arrangement of we can easily rearrange the fractions into descending order.

5/2, 8/5, 4/3, 11/10, 7/9, 5/8, 1/2, 1/3

This is required answer of given question.

## Conclusion:

In this article, we discussed the definition of an ordering fraction, also we discussed the techniques by using which we can easily rearrange the fractions, also we gave you the simple examples which is very helpful to understand the concept of ordering fractions.

After a complete reading of this article everyone would be able to understand the whole concept of ordering fraction and he/she would be able to easily tackle such these types of problems. Ordering fraction is a powerful tool which rearrange the fractions and kept it in order which is very helpful.

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