Relative numbers (part 2)

Multiplying Positive and Negatives numbers

We can only do arithmetic in the usual way.

To calculate 5(−2), we have to do 5· 2 = 10 — and then decide on the sign.

Is it +10 or −10?

For the answer, we have the following Rule of Signs.

Rules of signs

Like signs produce a positive number;

unlike signs, a negative number..

if the value of x is positive, then the value of −x must be negative, and vice-versa.

Since we call the positive or negative value of a number its sign, then we can state the following principle:

A minus sign changes the sign of a number.

On the number line, a minus sign reflects a number symmetrically about 0. You can observe it in the following picture:

segni opposti

When you multiply:

+ times + two positives make a positive:+ 3∙2=6

– times – two negatives make a positive: + (-3)∙(-2)=6

– times + a negative and a positive make anegative: (-3)∙(2)=-6

+ times – a positive and a negative make a negative: 3∙(-2)=-6

Formal rule:

A formal rule is simply a rule we write with letters. We write it with letters because we want it to apply to any numbers:

formal rule

Rule for 0:

Any number, multiplied by 0, gives 0 as a result.

a·0=0

Dividing Positive and negative numbers

Reciprocal: two numbers are reciprocals if their product is 1:

rec1.png

A division is a multiplication by the reciprocal:

rec2.png

When you divide, the rule is the same as for multiplication!

+ divided by + two positives make a positive: + 6÷2=3

– divided by- two negatives make a positive: + (-6)÷(-2)=3

– divided by+ a negative and a positive make a negative: (-6)÷(2)=-3

+ divided by- a positive and a negative make a negative: 6÷(-2)=-3

Exercises: (solutions at the end)

multdiv1.png

multdiv2

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