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Video: Expressing a Given Ratio in the Simplest Form

Tim Burnham

Express the ratio of 72 minutes to 30 minutes in its simplest form.

01:56

Video Transcript

Express the ratio of seventy-two minutes to thirty minutes in its simplest form. Now to express a ratio, we put those two numbers with a colon between them.

And the ratio doesn’t include the units, but it’s important to make sure that the numbers are in the same units to start off with, so we had seventy-two minutes and thirty minutes, so it’s okay to express the ratio in that way. If that was seventy-two hours to thirty minutes, then we wouldn’t be able to use the ratio seventy-two to thirty.

We’ll either have to convert them both to minutes or both to hours. Anyway, we don’t have that problem here, so our ratio is seventy-two to thirty. Now the question asked us to express that in its simplest form. And that simply means that have we got any common factors of seventy-two and thirty, which we can divide both of those numbers by to make an equivalent ratio.

Well they’re both certainly divisible by two, so an equivalent ratio half of seventy-two is thirty-six; a half of thirty is fifteen. So that’s a simpler ratio, but is it the simplest form? Well thirty-six and fifteen are both divisible by three.

Now thirty-six divided by three is twelve, and fifteen divided by three is five. And twelve and five don’t have any other common factors bigger than one, so that is in its simplest form. So the answer is, the ratio in its simplest form is twelve to five.

And just one thing before we go, the numbers were given to us in the order seventy-two to thirty, so it’s important that we kept the numbers that way round when we were simplifying our ratio.

So twelve to five is not the same as five to twelve, so if we’d have put five to twelve, we’d have got the wrong answer.