Lesson video

Hello.

My name is Mr. Clasper.

And today we are going to be adding and subtracting upper and lower bounds.

Let's begin with this example.

The length of a piece of ribbon is six centimetres to the nearest centimetre.

This diagram can represent our ribbon.

Five pieces of ribbon are placed end to end.

Now this diagram can represent our five pieces of ribbon.

What is the least possible total length of the ribbon? Well, in order to find this, we're going to need the lower bound for the length of our ribbon.

So as we're dealing with nearest centimetres, we need to place five centimetres at the left side of our number line and seven centimetres at the right side of our number line.

And if we calculate our mid points, we find that our lower bound is 5.

5.

This means that if each piece of ribbon was 5.

5 centimetres long, the least possible total length of the ribbon would be the sum of these five pieces of ribbon.

And this would give us 27.

5 centimetres.

What is the greatest possible total length of the ribbon? Well, let's calculate this.

We would need to use our upper bound.

The upper bound for the length of the ribbon is 6.

5.

So if we have five pieces of ribbon that are all 6.

5 centimetres long, this means the greatest possible total length of the ribbon would have to be 32.

5 centimetres.

Here's a question for you to try.

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

And here are your solutions.

So for one a, we needed to find the lower bound which was 10 foot and for part b, we needed to find the upper bound which was 14 foot for the total length.

And for question two, work out the greatest possible value of x plus x plus x plus x plus x or five lots of x, you should have found that this was 175.

So five lots of 35.

For the next example, we're going to calculate with the bounds of A and B.

So let's find the upper and lower bound of A.

And let's find the upper and lower bounds of B.

Now for the first question, we need to work out the lower and upper bound of A plus B.

Well, to do this, we would need to add the smallest possible value for A to the smallest possible value for B.

So this would mean that we're going to calculate 16.

15 plus 18.

5.

So these are the lower bounds of A and the lower bounds of B.

And this gives us 34.

65.

So the lower bound of A plus B is 34.

65.

To find the upper bound, we need to add our two upper bounds together.

So the upper bound of A plus the upper bound of B and this would give us 35.

75.

So the upper bound of A plus B is 35.

75.

For the next example, we're going to find the lower and upper bound of B subtract A.

When we subtract using bounds, we have to consider the problem in a slightly different way.

So to find the lower bound of B minus A, this would mean that we're looking for the smallest possible difference between A and B.

So if we think about our bounds to find the lower bound, we would need to find the difference between the lower bound of B and the upper bound of A as this would give us the smallest difference between the two.

So again, we're going to calculate the upper bound of A subtracted from the lower bound of B.

This would give us 2.

25.

Now, again, to find the upper bound of the same calculation, we need to find the largest possible difference.

This would be calculated from the upper bound of B subtract the lower bound of A.

So this would give us an upper bound of 3.

35 for the calculation of B minus A.

Here's some questions for you to try.

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

And here are your solutions.

So for question three, the correct solution was the bottom left.

So again, remember if we want the largest difference, we're going to need to subtract the lower bound of the smallest person from the upper bound of the largest person.

And for question four, to find the maximum amount of petrol he has left, we would need to start with the maximum amount of petrol or the upper bound, and we'd need to subtract the smallest possible amount of the petrol.

So we'd need to work out the lower bound for this.

And once we do this, we should end up with 3.

725 litres.

And that was the end of our lesson on adding and subtracting upper and lower bounds.

Want to give the exit quiz or go to show off your new skills.

I'll hopefully see you soon.