In the first part of the ratio section, we looked at a fruit bowl and created a ratio for the number of apples to bananas in the fruit bowl. Here was the fruit bowl.

From the above fruit bowl, we can see that the ratio between apples and bananas is 2:3. This means that for every two apples, there will be 3 bananas.

Whenever we create a ratio, we need to make sure that we have given the ratio in it’s simplest form. We simplify ratios by dividing all of the components of the ratio by the highest common factor of all of the components in the ratio. The ratio that we found for the fruit bowl example is already in it’s simplest form.

Let’s have a few examples.

Whenever we create a ratio, we need to make sure that we have given the ratio in it’s simplest form. We simplify ratios by dividing all of the components of the ratio by the highest common factor of all of the components in the ratio. The ratio that we found for the fruit bowl example is already in it’s simplest form.

Let’s have a few examples.

**Example 1**

Some sweets are shared between Andrew and Barry. Andrew gets 20 sweets and Barry gets 50 sweets. Create a ratio for the number of sweets that Andrew gets to the number of sweets that Barry gets.

We are wanting to find the ratio of the number of sweets that Andrew gets to the number of sweets that Barry gets. Therefore, we need to have the number of sweets that Andrew gets first, and then the number of sweets that Barry gets second.

Andrew gets 20 sweets and Barry gets 50 sweets. We sub these values into their appropriate places in the ratio.

The next step is to make sure that our ratios are given in their simplest form and we do this by dividing all of the components in the ratio by the highest common factor for all of the components in the ratio (dividing all of the components in the ratio by the highest common factor for all of the components will mean that the ratio goes straight to it’s simplest form. However, you can divide the components of the ratio by any common factor, and then check your answer to see if there are any more common factors for the components in the ratio).

The highest common factor for 20 and 50 is 10. Therefore, we divide both of the components of the ratio by 10. This results in the simplified ratio becoming:

The highest common factor for 20 and 50 is 10. Therefore, we divide both of the components of the ratio by 10. This results in the simplified ratio becoming:

Therefore, the ratio of sweets between Andrew and Barry is 2 : 5.

If you did not see that the highest common factor between 20 and 50 was 10, you could have divided by 2 because both 20 and 50 are even. Let’s divide both components of the ratio by 2.

If you did not see that the highest common factor between 20 and 50 was 10, you could have divided by 2 because both 20 and 50 are even. Let’s divide both components of the ratio by 2.

We then need to check whether there are any more common factors between 10 and 25. A common factor between 10 and 25 is 5, so we now divide both of the components in the ratio by 5.

There are no common factors between 2 and 5, which means that our ratio is now in its simplest form.

**Example 2**

Some money is shared out between 3 children; Sophie, Emily and Katie. Sophie is given £24, Emily is given £18 and Katie is given £42. Find a ratio for the amount of money that Sophie, Emily and Katie got.

The first step in answering this question is to write the names of the children in the order that the ratio wants them in. We are asked to find the ratio with Sophie first, then Emily and finally Katie.

The next step is to sub the amount of money that each child received. We are told that Sophie is given £24, Emily is given £18 and Katie is given £42. We sub these values in and the ratio becomes:

We now need to simplify the ratio, which we do by either dividing by the highest common factor to get straight to the simplified ratio, or by dividing by any common factor and then checking if there are any more common factors in the simplified result.

I am going to use the second method. All of the three components in the ratio are even and this means that they all have a common factor of 2. Therefore, I am going to divide all 3 of the components of the ratio by 2.

I am going to use the second method. All of the three components in the ratio are even and this means that they all have a common factor of 2. Therefore, I am going to divide all 3 of the components of the ratio by 2.

We now need to check if there are any more common factors between the 3 components of the ratio. 3 is a factor of all three of the components. Therefore, we divide all three of the components by 3.

We now check for any more common factors in the three components that are in the ratio. There are no more common factors, which means that we have found the ratio in it’s simplest form. The money is shared between Sophie, Emily and Katie in the ratio 4 : 3 : 7.

The other method of simplifying is dividing all 3 of the components in the ratio by the highest common factor of the 3 components. The highest common factor between 24, 18 and 42 is 6. Therefore, we could have gone straight to the simplified ratio by dividing all 3 of the components in the ratio by 6.

The other method of simplifying is dividing all 3 of the components in the ratio by the highest common factor of the 3 components. The highest common factor between 24, 18 and 42 is 6. Therefore, we could have gone straight to the simplified ratio by dividing all 3 of the components in the ratio by 6.