By now, you may have had a lot of practice in simplifying fractions and ratios into their simplest possible form by finding and applying the **Highest Common Factor (HCF)**.

One of the things that you may have heard is that you cannot have **decimals** in the simplified versions of ratios.

There is, however, **one** important exception to this rule.

You could be asked to write a ratio in the form **1:n** or **m:1**.

All this means is that either the first number must be** 1** (1:n) or the second must be **1 **(m:1).

This approach frequently means that you will have a **decimal** representing n or m.

In this situation alone, using a decimal in a ratio **is** allowed.

Let's look at this in action with some examples now.

**e.g. Write 5:8 in ****the form**** 1:n.**

As we are looking for **1:n**, this means that the** first **number in our ratio **must be 1** and the second can be a decimal or whatever we require.

Let's begin with our starting ratio:

5:8

In order to convert the** first** number to **1**, we have to **divide by 5** (as 5 ÷ 5 = 1).

So we need to do the same thing to the second number in the ratio:

5:8 ÷ 5 = **1 : 1.6**

**e.g. Write 25:10 in ****the form**** m:1.**

As we are looking for **m:1**, this means that the** second **number in our ratio **must be 1** and the first can be a decimal or whatever we require.

In order to convert the **second **number to **1**, we have to **divide by 10 **(as 10 ÷ 10 = 1).

25:10 ÷ 10 = **2.5 : 1**

In this activity, we will create and simplify ratios in the form 1:n or m:1 where the values of m and n can be decimals, converting values into the same units where required.