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70 percent of the surface area of the Earth is water. The rest of the surface area is land. Part a) Work out the ratio of water to land for the surface area of the Earth. Give your ratio in the form one to 𝑛.

If 70 percent of the surface area of the Earth is water, then this means that 30 percent of the surface area is land, as this is equal to 100 percent minus 70 percent. When we’re asked to work out a ratio, the order matters. So if we want the ratio of water to land, then we must write water first and then land. 70 percent of the Earth’s surface area is water, and 30 percent is land. So our ratio is 70 to 30.

We’ve been asked to give our ratio in a specific form. We’ve been asked to give it as one to 𝑛, which means we need to scale down the ratio so that it has a one on the left and some number 𝑛 on the right. To scale down from 70 to one, we need to divide by 70. So we need to do the same thing on the right of this ratio to make sure that our ratio is equivalent. We therefore have the ratio one to 30 over 70.

However, the fraction 30 over 70 can be canceled down, as both the numerator and the denominator can be divided by 10. And it leaves us with a fraction of three-sevenths. So the ratio of water to land for the surface area of the Earth in the form one to 𝑛 is one to three-sevenths.

Now this is a slightly unusual format in which to leave a ratio. Normally, we leave a ratio in its simplest form, which means that both parts of the ratio need to be integers or whole numbers with no common factors which we can divide by. However, as we’ve been asked to give our ratio in the form one to 𝑛, we must make sure our answer is in this format.

The ratio of water to land for the surface area of a different planet is one to six. Part b) What fraction of the surface area of this planet is water?

This ratio of one to six means that, for this different planet, its surface area is covered by one part water and six parts land. And remember, these are equal parts. There are a total of seven equal parts, as one plus six is equal to seven. The fraction of the surface area of this planet which is water is therefore one part out of seven parts, which we can write as one-seventh.