# Ordering Fractions. How to size order a set of fractions from smallest to biggest.

To order a set of fractions, from smallest to biggest, first you will need to make equivalent fractions that have the same denominator. To do this, find the least common multiple of all of the denominators. Once you have found the LCM then this will be denominator of each equivalent fraction.

**Example 1**

Sort these fractions into size order, starting with the smallest first:

5/6, 2/3, 7/10

Begin by writing down the first 10 multiplies of each denominator (6,3 and 10)

6,12,18,24,30,36,42,48,54,60

3,6,9,12,15,18,21,24,27,30

10,20,30,40,50,60,70,80,90,100

Now the smallest multiple which is common to all 3 lists is 30. So the least common multiple is 3.

Since we have now found the LCM, then you can now make some equivalent fractions with 30 on the denominator:

5/6 = 25/30 (multiply by 5)

2/3 = 20/30 (multiply by 10)

7/10 = 21/30 (multiply by 3)

The fractions are now easy to sort out in size order as you just need to look at the numerators of the equivalent fractions:

20/30, 21/30 and 25/30

All you need to do now is write down the original fractions in size order:

2/3, 7/10 and 5/6

**Example 2**

Sort these fractions into size order, starting with the smallest first:

2/5, 3/10, 7/25, 9/20

First find the least common multiple of all of the denominators. This number is 100, as 100 is in the 5, 10, 25 and 20 times tables.

Since we have now found the LCM, then you can now make some equivalent fractions with 100 on the denominator:

2/5 = 40/100 (multiply by 20)

3/10 = 30/100 (multiply by 10)

7/25 = 28/100 (multiply by 4)

9/20 = 45/100 (multiply by 5)

The fractions are now easy to sort out in size order as you just need to look at the numerators of the equivalent fractions:

28/100, 30/100, 40/100 and 45/100

All you need to do now is write down the original fractions:

7/25,3/10,2/5 and 9/20

So that is all you need to do when writing fractions in size order – just convert all of the fractions so that they have the same denominators. An alternative method to this is to convert the fractions into decimals or percentages, but you will probably need to rely on your calculator a little more to do this.