Percentages

A percentage means out of 100. For example, 25 percent means 25 out of 100 or 25 divided by a 100. Seven percent means seven divided by a 100 or seven out of 100. And 98 percent means 98 out of 100 or 98 divided by 100. Let’s start by changing percentages into fractions. So the first one, 75 percent is 75 divided by 100. What we need to do is to break that down into smaller numbers, in other words we’re simplifying the fraction, so let’s divide by 25, top and bottom, and we get three divided by four, so 75 percent, as a fraction is three-quarters, similarly 40 percent is 40 divided by 100. Notice here that there are zeroes top and bottom, cancel one on the top with one on the bottom, that leaves us with four over 10 which cancels even further into two over five, so 40 percent is two-fifths.

Let’s look at a large percentage and change this to a fraction, 175 percent is the same as 175 divided by 100, but now we turn this into a mixed fraction, which is one and 75 over 100. Notice again that 75 over 100 can be cancelled down, so we divided both top and bottom by 25 leaving us with an answer of one and three-quarters. So 175 percent is one and three-quarters.

Now let’s change a decimal percentage into a fraction. For instance we have the percentage 17.5 percent, which is 17.5 over 100. What we need to do here is to turn that 17.5 into a whole number so that we can then cancel the terms down. So we’re multiplying 17.5 by 10 and doing that to the top we must do the same thing to the bottom. In other words 17.5 by 10 is 175, 100 times 10 is 1,000, now we look to see if anything cancels and of course it does, we can divide both top and bottom by 25 leaving us with an answer of seven over 40, so 17.5 percent is seven over 40 as a fraction.

Now let’s look at a small decimal percentage. We have here 1.25 percent, which is the same as 1.25 divided by 100, again we need to turn the 1.25 into a whole number so this time we multiply it by 100 because 1.25 has got two decimal places and similarly we must multiply the denominator by 100 as well, so the top line becomes 125, the bottom line becomes 10,000, which cancels down into one over 80, so 1.25 percent is one over 80 as a fraction.

Now let’s change percentages into decimals. An example, 15 percent is the same as 15 over 100, change a percentage into a decimal we always move the decimal point two places to the left, so if you move the decimal point two places to the left we end up with 0.15. Similarly with a large percentage, 220 percent is the same as 220 divided by 100, so the quick way to do this is to move the decimal point two places to the left, so we end up with an answer of 2.2. So 220 percent is 2.2 as a decimal.

Finally 7.9 percent is 7.9 divided by 100 and dividing by 100 you simply move the decimal point two places to the left, so moving it two places to the left leaves us with an answer of 0.079, so 7.9 percent is 0.079.

Now let’s change fractions into percentages. So here we’re working in reverse to what we were doing in previous slides. Here’s an example, seven over 10. To change a fraction into a percentage we always multiply it by 100 and because the fraction is written as seven over 10 we can write the 100 as a fraction as well, 100 over one. Notice that one zero on the top will cancel with one zero on the bottom, in other words I’m dividing by 10, which leaves us with 70 over one, which gives us an answer of 70 percent. In other words seven-tenths is 70 percent as a percentage.

How about changing decimals into percentages, well we use the same idea as before. Here’s an example, 0.55, to change that decimal into a percentage we multiply it by 100 and when you multiply by 100 what you’re actually doing is you’re moving the decimal point two places to the right, so we start at the decimal point, move two places and we finish after the last digit, the five in this case. So we have an answer of 55, which is 55 percent, so 0.55 is 55 percent as a percentage.

What about small decimals, changing those into percentages. We use exactly the same rule as before. Here’s an example, 0.09, to change that into a percentage we multiply by 100, so again, as before, we’re moving the decimal point two places to the right and here the decimal point ends up on the far right hand side after the last digit, the nine, so our answer is nine percent, so 0.09 is nine percent as a percentage.

Now try some problems for yourself. The answers to these questions are on the next slide. Thanks for watching this short movie.