Multiplying Negative Numbers © T Madas.

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Presentation transcript:

Multiplying Negative Numbers © T Madas

© T Madas

© T Madas

5 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 © T Madas

The 2 times table Follow the pattern 4 8 3 6 The 2 times table 2 4 1 2 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 Follow the pattern -2 -4 -3 -6 -4 -8 -5 -10 © T Madas

The 3 times table Follow the pattern 4 8 12 3 6 9 The 3 times table 2 4 6 1 2 3 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 Follow the pattern -2 -4 -6 -3 -6 -9 -4 -8 -12 -5 -10 -15 © T Madas

The 4 times table Follow the pattern 8 12 16 3 6 9 12 The 4 times table 2 4 6 8 1 2 3 4 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 Follow the pattern -2 -4 -6 -8 -3 -6 -9 -12 -4 -8 -12 -16 -5 -10 -15 -20 © T Madas

4 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10 So far 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 2 0 times table 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 8 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10 0 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

0 times table Follow the pattern 4 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10 0 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 Follow the pattern -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 2 1 times table 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 8 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10 1 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

1 times table Follow the pattern 4 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10 1 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 Follow the pattern -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 2 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 8 4 8 12 16 20 3 3 6 9 12 15 2 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

2 times table Follow the pattern 4 4 8 12 16 20 3 3 6 9 12 15 2 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 Follow the pattern -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 3 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 8 4 8 12 16 20 3 3 6 9 12 15 3 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

3 times table Follow the pattern 4 4 8 12 16 20 3 3 6 9 12 15 3 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 Follow the pattern -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 4 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 8 4 8 12 16 20 3 3 6 9 12 15 4 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 times table Follow the pattern 4 8 12 16 20 3 3 6 9 12 15 4 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 Follow the pattern -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 5 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 8 4 8 12 16 20 3 3 6 9 12 15 5 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

5 times table Follow the pattern 4 4 8 12 16 20 3 3 6 9 12 15 5 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 Follow the pattern -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

So far we continued the patterns vertically 4 4 8 12 16 20 3 3 6 9 12 15 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 So far we continued the patterns vertically Can we see any patterns horizontally? -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 2 1 2 times table -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 8 4 8 12 16 20 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 1 1 2 3 4 5 2 times table -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 2 3 times table 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 4 8 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 3 times table 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

4 3 4 times table 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 -24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 4 times table 2 2 4 6 8 10 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

We filled ¾ of our table 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 We filled ¾ of our table We can fill the bottom left corner by following the patterns vertically or horizontally -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -1 -2 -3 -4 -5 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

Horizontally 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 -24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 Horizontally -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 -3 -3 -6 -9 -12 -15 -4 -4 -8 -12 -16 -20 -5 -5 -10 -15 -20 -25 © T Madas

Vertically 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 -24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 Vertically 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 6 -3 -3 -6 -9 -12 -15 8 -4 -4 -8 -12 -16 -20 10 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 9 6 -3 -3 -6 -9 -12 -15 12 8 -4 -4 -8 -12 -16 -20 15 10 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 12 9 6 -3 -3 -6 -9 -12 -15 16 12 8 -4 -4 -8 -12 -16 -20 20 15 10 -5 -5 -10 -15 -20 -25 © T Madas

We can try a few horizontal patterns again -24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 We can try a few horizontal patterns again -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 12 9 6 -3 -3 -6 -9 -12 -15 16 12 8 -4 -4 -8 -12 -16 -20 20 15 10 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 18 15 12 9 6 3 -3 -3 -6 -9 -12 -15 16 12 8 -4 -4 -8 -12 -16 -20 20 15 10 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 18 15 12 9 6 3 -3 -3 -6 -9 -12 -15 24 20 16 12 8 4 -4 -4 -8 -12 -16 -20 20 15 10 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 4 3 2 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 18 15 12 9 6 3 -3 -3 -6 -9 -12 -15 24 20 16 12 8 4 -4 -4 -8 -12 -16 -20 30 25 20 15 10 5 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 5 4 3 2 1 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 18 15 12 9 6 3 -3 -3 -6 -9 -12 -15 24 20 16 12 8 4 -4 -4 -8 -12 -16 -20 30 25 20 15 10 5 -5 -5 -10 -15 -20 -25 © T Madas

-24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 5 4 3 2 1 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 18 15 12 9 6 3 -3 -3 -6 -9 -12 -15 24 20 16 12 8 4 -4 -4 -8 -12 -16 -20 30 25 20 15 10 5 -5 -5 -10 -15 -20 -25 © T Madas

Let’s use this table © T Madas

And that is maths’ magic 1 -24 -20 -16 -12 -8 -4 4 4 8 12 16 20 -18 -15 -12 -8 -6 -3 3 3 6 9 12 15 -12 -10 -8 -6 -4 -2 2 2 4 6 8 10 And that is maths’ magic -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 5 4 3 2 1 -1 -1 -2 -3 -4 -5 12 10 8 6 4 2 -2 -2 -4 -6 -8 -10 18 15 12 9 6 3 -3 -3 -6 -9 -12 -15 24 20 16 12 8 4 -4 -4 -8 -12 -16 -20 30 25 20 15 10 5 -5 -5 -10 -15 -20 -25 © T Madas

It was hard work making all these slides… I must start getting out more © T Madas

Negative Numbers Formal Proofs © T Madas

© T Madas

© T Madas

© T Madas

© T Madas