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Hello.

My name is Mr. Clasper.

Today, we are going to be looking at inverse proportion.

Y is inversely proportional to X.

This means as one value increases, the other value decreases at the same rate.

We can say, that Y is directly proportional to one over X.

This is because if we multiplied by one over X, this would be the inverse of multiplying by X.

So for example, if I take a value and multiply it by X, then multiply that value by one over X, I have the same value I started with.

Therefore, we can say that Y is directly proportional to one over X.

Let's have a look at this with some numbers.

Can you spot any patterns in this table? Well, if you look carefully, you can see that the value of y doubles as the value of x halves, or in other words, it decreases at the same rate as y increases.

So the value is given for y have been multiplied by two each time.

And the values for x have been multiplied by one over two each time or divided by two.

Here is a typical example m is inversely proportional to n if m is equal to 10, when n is equal to four, find m when n is equal to eight.

What do you think the answer will be? Let's have a look.

The first thing we could do is to write an equation.

So this time our equation will be m is equal to k over n.

Then we can substitute our values.

So we know that when m is equal to 10 and n is equal to four.

So that must mean that 10 is equal to k over 4 and therefore k or our constant of proportionality must be equal to 40.

Now we have a formula we can use.

From this, we're asked to find m when n is equal to eight.

So if we substitute n is equal to eight into the formula, we get 40 divided by eight, which means that m must be five.

Did you get that answer? m is inversely proportional to n squared.

If m is equal to 10, when n is equal to four, find m when n is equal to eight.

What's the same and what's different in this example? While we're using the same values for m and n and our value for n is doubled, to find out a different value of n.

However, the statement says, m is inversely proportional to n squared.

This is the main difference.

What do you think the answer will be this time? Let's have a look.

This is the equation we can write.

We have m is equal to k over n squared, and we're going to substitute our values for m and n.

So remember, we're going to square n which gives us 10 is equal to k over 16.

And therefore my constant of proportionality must be 160.

And now I have the formula m is equal to 160 over n squared.

My next step is to find the value of m which is two point five.

So if we calculate 160 divided by eight squared, this gives us a value for m of two point five.

Can you see why the answer is two point five? In the first example, when we doubled the value for n this halved the value for m.

So when we multiplied n by two, we divided m by two.

Whereas in the second example, even though we've multiplied the value for n by two, because this is going to be squared, this would mean that our value for m would need to be divided by two squared or four.

So 10 divided by four would give us our two point five.

Here's some questions for you to try pause the video, to complete your task and click resume once you're finished On to your solutions.

So for each of these questions, you need to make sure that you have an equation in the form of y is equal to k over x.

And you're going to need to find the constant of proportionality in each case.

So you should have, y is equal to 12 over x.

So the constant of proportionality was 12 for question one, and for question two, you should have m is equal to 30 over n and the constant of proportionality that is 30.

And if you substitute your value for n into this, you will find that m is equal to six.

For part B.

The question says, what happens to the value of n if you double the value of m because they are inversely proportional? This means that if m doubles then n must half, therefore the value then would be one point five in this case.

On to your last two questions.

Pause the video to complete your task and click resume once you're finished.

And here are your solutions for question three and four.

So just ensure that you read these questions carefully.

So the first one, y is inversely proportional to x squared? This means that our formula is going to be in the form of y is equal to k over x squared.

And when you substitute your value for x, for part B, just make sure that you square this, and you should end up with a value of y is equal to nine for part B, and value of x is equal to six for part C.

And likewise, for question four, if we read this carefully, h is inversely proportional to the square root of t.

So this would give us, y is equal to k over the square root of t.

And you should find that your constant of proportionality is 35, giving you h is equal to 35 over the root of t.

And that wraps up our lesson on inverse proportion.

Why don't I give the exit quiz a go to show off your new skills? I'll hopefully see you soon.