Question Video: Expressing a Given Ratio in Its Simplest Form Mathematics

Express the ratio 72 : 54 : 81 in its simplest form.

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Video Transcript

Express the ratio 72 to 54 to 81 in its simplest form.

To do this, we need to find something that 72, 54, and 81 are all divisible by. I noticed that all three of these values are multiples of nine, which means we can divide all three of these values by nine. And that will keep their ratio equivalent. 72 divided by nine equals eight. 54 divided by nine equals six. And 81 divided by nine equals nine. The new ratio is then eight to six to nine.

It’s important that we remember here when dealing with ratios, the order cannot be changed. It must be the order that we found it. But what if you didn’t recognize that all three of these values were divisible by nine? But you did notice that they were divisible by three. If you notice that they were all divisible by three, you would get the ratio 24 to 18 to 27. At which point you should notice that 24, 18, and 27 are also all divisible by three, which means you can divide them by three again, which would give you eight to six to nine. Exactly as we found the first time.

We know that this is the simplest form because eight, six, and nine do not share any more factors.

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