**Example 1**

Place the following fractions in ascending order.

To answer this question, we are going to be creating equivalent fractions where all of the denominators are the same. The new denominator for the fraction will be the lowest common multiple between all of the denominators involved; the lowest common multiple is the smallest number that is a multiple of two or more given numbers. There are 3 different denominators; 2, 4 and 8. The lowest common multiple between these 3 numbers is the lowest number that 2, 4 and 8 go into, which is 8. The next step is to create equivalent that all have 8 as their denominator.

Whenever we are creating equivalent fractions, we multiply the numerator and the denominator of the fraction by the same value. The first fraction is ½. The denominator of this fraction is 2 and the denominator of the new fraction will be 8. To find out what we have multiplied the denominator by, we divide the new denominator (8) by the original denominator (2), which is 4. We now multiply the original numerator by 4. The equivalent fraction to ½ becomes ^{4}/_{8}.

We now do the same for the other 4 fractions in the question. The second and fifth fraction already have the denominator of 8, which means that we do not need to do anything to them.

We now have all of the fractions with a denominator of 8.

We can arrange the equivalent fractions by having the lowest numerator first and the highest numerator last.

We just need to remember to give our answer with the original fractions rather than our equivalent fractions.

**Example 2**

Place the fractions below in descending order.

The first step is to create equivalent fractions with the same denominators. The denominators of the new fractions are going to be the lowest common multiple of all of the current denominators. Therefore, we are looking for the lowest possible number that 10, 3, 15, 30, 2 and 5 go into. It is usually best to start with the highest current denominator and see whether all of the other denominators are a factor of the highest current denominator. The highest current denominator is 30; 10 is a factor of 30, 3 is a factor of 30, 15 is a factor of 30, 2 is a factor of 30 and 5 is a factor of 30. Therefore, the lowest common multiple for all of the denominators is 30.

The next step is to create equivalent fractions with the denominators of 30.

In order to get the denominator of the first fraction to equal 30, we need to multiply by 3 (new denominator ÷ original denominator: 30 ÷ 10 = 3). Therefore, the first fraction becomes 9/30.

We need to multiply the second fraction by 10, which means that the fraction becomes ^{20}/_{30}.

The third fraction needs to double, which means that the fraction becomes ^{22}/_{30}.

The fourth fraction already has a denominator of 30, which means that we do not need to do anything to it.

The fifth fraction needs to be multiplied by 12, which means that the fraction becomes ^{15}/_{30}.

The final fraction needs to be multiplied by 6 and this means that it becomes ^{24}/_{30}.

The original and new fractions are given below.

The question is asking us to place the fractions in descending order. As all of the denominators of the fractions are the same, we can order the fractions in descending order by placing the fraction with the highest numerator first and the lowest numerator last.