Lesson video
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Hello, my name is Mr Clasper.
And today, we are going to be multiplying and dividing using upper and lower bounds.
The length of a piece of ribbon is six centimetres to the nearest centimetre.
Let this represent the ribbon.
25 pieces of ribbon are placed end-to-end.
What was the least possible total length of the ribbon? To calculate this, we're going to need the lower bound of our piece of ribbon.
So the smallest possible measurement, our piece of ribbon could take would be 5.
5 centimetres.
If we assume each piece of ribbon is 5.
5 centimetres, we can calculate 25 multiplied by 5.
5, as we have 25 lots of 5.
5.
This would give us 137.
5 centimetres as the least possible total length of the ribbon.
What is the greatest possible total length of the ribbon? Well, for this, we need our upper bound, which is 6.
5.
So if we assume that each piece of ribbon is 6.
5 centimetres long, we would calculate 25 multiplied by 6.
5.
And this would give us a greatest possible total length of 162.
5 centimetres.
Let's take a look at this problem.
The length of a piece of ribbon is six centimetres to the nearest centimetre.
Some pieces of ribbon are place end-to-end.
The total length of the pieces of ribbon is at least 33 centimetres.
Here's a diagram we could use.
What is the maximum number of pieces of ribbon there could be? To do this, we're going to need to use bounds.
And we're going to use the lower bound.
This is because we need to find out how many pieces of the smallest length of ribbon can be placed end-to-end to create a total length, which is at least 33 centimetres.
As this will give us the largest number of pieces there could be.
Therefore, I'm going to calculate 33 divided by 5.
5, this gives me six.
Therefore the maximum number of pieces of ribbon there could be is six.
Here are 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 one, you needed to multiply your upper bound by 20 to get your solution.
And for question two, we need to calculate 120 divided by the lower bound, which would give us eight strips.
Work out the lower and upper bound of AB, or A multiplied by B.
To do this, we're going to need our bounds first of all.
The lower bound of AB will be the lower bound of A, multiplied by the lower bound of B.
This means the lower bound of AB is 298.
775.
To calculate the upper bound, I need to multiply the upper bound of A by the upper bound of B.
This gives an upper bound for AB of 316.
875.
In the next example, we're going to be finding the lower and upper bound of A divided by B.
Let's take a look at these four calculations.
The first is the lower bound of A, divided by the lower bound of B.
The second is the lower bound of A, divided by the upper bound of B.
The third is the upper bound of A, divided by the lower bound of B.
And the last is the upper bound of A, divided by the upper bound of B.
To find the lower bound of A over B, we need to find the smallest possible value, which is this one here.
And this makes sense because we've taken the smallest possible starting value for A and divided it by the largest possible value for B.
Likewise, my upper bound is the highest value, which is this one.
And again, this makes sense as we've taken the highest possible value for A and divided it by the smallest possible value for B.
Therefore my lower bound is 0.
8282051.
And my upper bound is 0.
8783.
Here's your last question.
Pause the video to complete your task and click resume once you're finished.
And here are your solutions.
So remember to calculate the area of the rectangle, we multiply the length by the witch.
So to work out the upper bound for the area, we need to multiply the upper bound of the length by the upper bound of the width.
And for part b, we need to multiply the lower bound for the length by the lower bound for the width.
And that's the end of our lesson.
So now we've been multiplying and dividing using upper and lower bounds.
why don't you give the exit quiz a go to show off your new skills? I'll hopefully see you soon.
