1TH/vwo §8.4 Multiplying and division

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

§8.4 

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.

funny witch - strange brews ...

Remember the witch? From all the strange brews.

Once upon a day she wants to work quicker

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.

Think about this and answer in the next slide.

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

1. rise
2. fall
3. stay the same

Answer:

Adding COLD BLOCKS make 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.

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 falls by 3 degrees
2. it rises by 3 degrees
3. it falls by 15 degrees
4. it rises by 15 degrees

Solution:

This is a bit tricky!

Removing cold blocks makes it LESS COLD  in the kettle.

So it gets 5 x 3 = 15 degrees WARMER!

Task: 

answer c, below, in the next slide.

removing a bucket of 3 cold blocks 5 times
gives this calculation:

Solution Task c:

- 5 x -3 = 15                           So: minus times minus is positive.                                              or:                                                    -            x            -        =      +

' -3 '   means 3 COLD Blocks and

'-5'      means 5 buckets are REMOVED from the cauldron.

1. 50-55
2. 55-60
3. 60-65
4. 65-70

Question : What mistake was made in the 2nd line? ('removed 6 times .......')

The mistake in the second line is:

-6 x 8 = ....    this wrong, as it read that there were 8 COLD blocks!

-6 x -8 = 48     is what it should've been!

Now a little joke.

The funny part is this:

To have been around the block means also:

to have a lot of experience with something!

Let's discuss this table.

First ALL THINK ABOUT the 1st line. Then ONE GETS THE TURN to explain it.

Then we do the same with the 2nd line, etcetera.

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.

In short we write it as follows:

+    :    + =    +

+   :     -   =   -

-    :    +   =   -

-    :   -    =   +  

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

SOLUTION:

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:

HV1Y:      §8.4.   not 25 and 26

Homework:

HV1Y:                             30 t/m 35 S 30 and S32, p.63

G1X, A1X and C1X:    30 t/m 35 also do C7 +  C8,  p.63

That's all, folks!