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MatematikaRia.com

# Multiplying Negatives

## When You Multiply ...

 Example × two positives you get a positive: 3 × 2 = 6 × a positive and a negative you get a negative: (-3) × 2 = -6 × a negative and a positive you get a negative: 3 × (-2) = -6 × two negatives you get a positive: (-3) × (-2) = 6

So, a negative times a positive gives a negative ...
but multiplying two negatives gives a positive!

## Why does multiplying two negative numbers make a positive?

Well, first there is the "common sense" explanation:

If I say "Eat!" I am encouraging you to eat (positive), but if I say "do not eat!" I am saying the opposite (negative).

Now if I say "Do NOT not eat", I am saying I don't want you to starve, so I am back to saying "Eat!".

So, two negatives make a positive, and if that satisifes you, then you don't need to read any more.

## Direction

It is all about direction. Remember the Number Line? Well here we have Baby Steven taking his first steps. He takes 2 paces at a time, and does this three times, so he moves 3 x 2 = 6 steps forward: Now, Baby Steven can also step backwards (he is a clever little guy). His Dad puts him back at the start and then Steven steps backwards 2 steps, and does this three times: Once again Steven's Dad puts him back at the start, but facing the other way. Steven takes 2 steps forward (for him!) but he is heading in the negative direction. He does this 3 times: Back at the start again (thanks Dad!), still facing in the negative direction, he tries his backwards walking, once again taking two steps at a time, and he does this three times: So, by walking backwards, while facing in the negative direction, he moves in the positive direction.

## More Examples

### Money Owed vs Money Owned

Example: You owe 3 people \$5 each. So you are "Negative 15" (3 × -5 = -15).

They then say "we like you so much we forgive the debt" ... you have just had 3 subtractions of -5, so you are \$15 better off (-3 × -5 = +15).

### Tank Levels Rising/Falling

Example: The tank has 30,000 litres, and 1,000 litres are taken out every day. What was the level 3 days ago?

We know the tank has -1,000 every day, and we need to subtract that 3 times, so the change will be:

-3 × -1,000 = +3,000

The full calculation is:

30,000 + (-3 × -1,000) = 30,000 + 3,000 = 33,000

And That's All !