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This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Fractions, Decimals, and Percentages. Join the course to learn more.
6.6

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds PAULA KELLY: So let’s have a look, now, at trying to express a fraction as a percentage. So we have, here, a box of chocolates. We know that 12 are milk, 13 are white.

Skip to 0 minutes and 18 seconds MICHAEL ANDERSON: OK, and we want to know what percentage of the chocolates are milk chocolate.

Skip to 0 minutes and 23 seconds PAULA KELLY: Yeah, very good. OK, so we have 12 milk chocolates out of 25 chocolates.

Skip to 0 minutes and 31 seconds MICHAEL ANDERSON: Where did you get the 25 from?

Skip to 0 minutes and 33 seconds PAULA KELLY: So I know that I’ve got 12 milk, 13 white, and my whole box, 25.

Skip to 0 minutes and 38 seconds MICHAEL ANDERSON: Says that on the packet, as well.

Skip to 0 minutes and 40 seconds PAULA KELLY: Also quite a common misconception to have 12 out of 13, so it’s good to be really clear about this. So in total, there are 25, so be very clear, OK? If I want a percentage, we need that percentage– percent– is out of 100. So it’d be really useful if our fraction could be out of 100.

Skip to 0 minutes and 57 seconds MICHAEL ANDERSON: OK, yeah. That makes sense.

Skip to 1 minute and 0 seconds PAULA KELLY: So if we’re keeping an equivalent fraction, if I know I need to multiply this by 4– because 4/25 will give me 100– I also need to multiply 12 by 4 to keep it equivalent.

Skip to 1 minute and 13 seconds MICHAEL ANDERSON: OK, yeah. That makes sense.

Skip to 1 minute and 16 seconds PAULA KELLY: So 12/4, I know, are 48.

Skip to 1 minute and 21 seconds We’re still not quite there, though. We still have our fraction. I need a percentage. So we know that our fraction line is a division. If we do 48 divided by 100, all our numbers will go 2 places smaller. So we do know that 48 out of 100 is the same as if we divide by 100– 0.48. Still in our percentage, but we know percent– parts of 100. If we multiply this by 100, we come up with 48%.

Skip to 1 minute and 57 seconds MICHAEL ANDERSON: So percent is just out of 100. We’ve got 48 over 100, so it’s 48%.

Skip to 2 minutes and 2 seconds MICHAEL ANDERSON: I’ve seen one other way of possibly working this out, especially if I’ve got a calculator. If I just put into my calculator 12 divided by 25, then hopefully, as a decimal, that would give me 0.48, and I convert that into a percentage, so it’s 48%.

Skip to 2 minutes and 19 seconds PAULA KELLY: Perfect. OK, so let’s have another look at how we can write an amount as a fraction, but also the percentage. So we have here you would like to know which percentage of teams play in red kit. We have 9 teams out of a total of 20 teams.

Skip to 2 minutes and 37 seconds MICHAEL ANDERSON: And the 9 teams play in red, and then the other 11 teams play in different colours?

Skip to 2 minutes and 41 seconds PAULA KELLY: Absolutely. OK, so that leads us, quite naturally, into a fraction. We’ve got 9 out of 20 altogether. We’d like a percentage. At the moment, it’s not immediately obvious what percentage that would be. So percentage– parts of 100. Ideally, we have a denominator of 100.

Skip to 3 minutes and 4 seconds PAULA KELLY: If I’ve had to multiply this by 5– because I know five 20’s are 100– I’ve got to do the same thing to my numerator. I multiply that by 5, nine 5’s are 45.

Skip to 3 minutes and 21 seconds So I know that 45 out of 100 is 45%. But let’s see why that works. So if we had 45 out of 100, we know that our fraction line of division– 45 divided by 100– our numbers get 2 places smaller. We can write as a decimal as 0.45. Again, percent– out of 100. We multiply by 100. That just gives us a 45%.

Skip to 3 minutes and 54 seconds MICHAEL ANDERSON: 45 out of 100. And again, I suppose if I had a calculator, I could do this slightly differently. 9 teams playing red out of 20, so 9 over 20 as a division, 9 divided by 20. If I put that in a calculator, it will give me 0.45, which then is equivalent to 45%.

# Expressing one amount as a percentage of another

When comparing proportions it is very useful to express one amount as a percentage of another. For example, if 10 out of 28 girls are left-handed and 7 out of 22 boys are left-handed, which is the largest, the proportion of girls who are left-handed or the proportion of boys who are left-handed?

Often this technique is learnt: “take one number, divided by another number, then times that by a hundred”, without a real understanding of what is being done, and why it is being done.

In this video we explore simple methods of expressing one amount as a percentage of another which attempt to explain what is being achieved and to develop an understanding of why ‘the rule’ works. The examples are carefully chosen so as to easily scale up to form a fraction out of a hundred.

## Problem worksheet

Now complete question six from this week’s worksheet, but only those parts which are easily scalable to be out of a hundred.

In the next step we use techniques developed in the proportional reasoning course to look at the process when the numbers are not as simple to scale up.