1Tvwo §8.4 Multiplication and division

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

It is good to realise that x  and  :  are each others reverse!

For example:

48 : 8 = 6,  because 6 x 8 = 48 !

In this LessonUp you will get:

+ new Information and

+ also quite a few short Tasks, to Practise this new Information.

Remember the witch with the soup?

Once upon a time she wants to work more handy

with her cold and hot blocks.

She wants to put in or take out MORE temperature blocks

IN ONE GO! 

For this she uses a BUCKET.

This is what this § is about.

When you add or remove a larger number of blocks in one go:

Think about this and answer in the next slide:

You add a bucket of 6 cold blocks four times.

Does the temperature rise or fall?

By how many degrees?

Adding a buckets of 6 cold blocks
4 times makes the temperature in the cauldron ...

1. rise
2. fall
3. stay the same

Answer:

Adding COLD BLOCKS makes the temperature fall.

NEW QUESTION: By how many degrees does it fall?

Remember: she adds 6 cold blocks 4 times!

Answer in the next slide!

Adding 6 cold blocks 4 times make the temperature fall by ... degrees.

1. 24
2. -24
3. 6
4. -6

SOLUTION:

The temperature gets lower, of course!

However, it falls by 24 degrees and not by -24 degrees.

In other words: is gets colder by 24 degrees.

What happens to the temperature if 3 Cold Blocks are REMOVED 5 times?

Think about it carefully.

Answer in the next slide again.

What happens to the temperature if 3 Cold Blocks are REMOVED 5 times?

1. it drops by 3 degrees
2. it rises by 3 degrees
3. it drops by 15 degrees
4. it rises by 15 degrees

removing 5 times 3 cold blocks:

Solution:

This is a bit tricky!

Removing cold blocks makes it LESS COLD  in the kettle.

out 5 times three cold blocks = 

- 5  x  -3 => it gets 5 times less cold because you remove cold blocks

So it gets 5 x 3 = 15 degrees WARMER!

Let's do this one together. 

Exercise 26

Above you see the Basic Rules for Multiplying with

Positive and Negative Numbers.

Realise that you can always relate all these Calculations to:     

Hot and Cold Blocks in a number of Buckets, that are added or removed from the kettle!

The reverse of multiplying is ....

dividing!

Key in your answer in the next slide!

24 : -8 = -3, because ....
(make the multiplication!)

1. 3 x -8 = -24
2. -3 x 8 = -24
3. -3 x -8 = 24
4. 3 x 8 = 24

                       Solution:

                       -3 x -8 = 24

In this way, we can make Basic Rules for all 4 types of 

divisions (=delingen) with positive and negative numbers!

See next slide.

Think about it.

Key in your answer in the next slide!

-18 : -9 = ......
because ..... x ..... = .....

The Numbers to be filled in are:

1. -2, -2, 9, 18
2. -2, -2, -9, -18
3. 2, -2, -9, 18
4. 2, 2, -9, -18

We just learned that:

 a negative number divided by a negative number is a positive number.

So            - 18 : -9 = 2, because 2 x -9 = -18  !

Homework:

Do 8.4 the Challenge path

Check your results with the solutionsbook (see Teams)

Learning goals reached?

I can multiply with negative numbers

I can devide with negative numbers

0,5 x - 12 - 4 =

1. -8
2. -10
3. 8
4. 2

- 99 - 81 : - 9 =

1. -90
2. 90
3. -20
4. 20