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3.3 B) Simplifying Ratio – Part 2
3.3 B) Simplifying Ratio – Part 2
This section builds on the content that we have looked at in the first section of ratios, so make sure that you give that section a go first before working your way through this section (click here to be taken through to the section before). In the previous section, we learnt that we should always give ratios in their simplest form and we get them in their simplest form in a similar way to simplifying fractions; we find the highest common factor that appears in all of the different components of the ratio and then divide each of the components in the ratio by the highest common factor that we have found.
In addition to simplifying ratios, we need to make sure that our ratios are given in integer form. Let’s have an example where we are given a ratio with a decimal and asked to simplify it.
In addition to simplifying ratios, we need to make sure that our ratios are given in integer form. Let’s have an example where we are given a ratio with a decimal and asked to simplify it.
Example 1
In order to make eggless cakes, we need 0.6 kg of flour, 0.2 kg of butter and 0.4kg of sugar. Give this ratio in its simplest form whereby all of the components in the ratio are integers.
Let’s start by creating the ratio whereby we have decimals in our answer. The ratio of flour to butter to sugar is:
In order to make eggless cakes, we need 0.6 kg of flour, 0.2 kg of butter and 0.4kg of sugar. Give this ratio in its simplest form whereby all of the components in the ratio are integers.
Let’s start by creating the ratio whereby we have decimals in our answer. The ratio of flour to butter to sugar is:
We want to have this ratio with integers and no decimals. Currently all of these decimals are in tenths. We are able to take them out of tenths by multiplying all of the three components by 10. The ratio then becomes:
The three terms are now all integers (whole number). We now need to check that the ratio is given in its simplest form. We do this by seeing if there are any common factors between the 3 different components in the ratio and dividing the three terms by the highest common factor that we see. When we check for common factors, we see that the highest common factor between 6, 2 and 4 is 2. Therefore, we divide each of the components in the ratio by 2 and the ratio becomes:
(This was a fairly straightforward question to find the highest common factor between 6, 2 and 4, but if the numbers were a little bit harder, you could divide the three components by any common factor and then check the ratio that you obtain to see if the ratio can be simplified further).
The ratio of flour to butter to sugar is 3 : 1 : 2.
The ratio of flour to butter to sugar is 3 : 1 : 2.
Example 2
Simplify the following ratio:
Simplify the following ratio:
The easiest way to get rid of a half is to double everything. When we multiply every term by 2, the ratio becomes:
All of the terms in the ratio are now integers, but they are not in their simplest form and this means that we need to find the highest common factor between the three components of the ratio and divide each of the three components of the ratio by the highest common factor. The highest common factor between 20, 5 and 15 is 5, so we divide each of the three components by 5. Our ratio becomes:
This ratio is now in its simplest form.