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:
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
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:
Rule for 0:
Any number, multiplied by 0, gives 0 as a result.
Dividing Positive and negative numbers
Reciprocal: two numbers are reciprocals if their product is 1:
A division is a multiplication by the reciprocal:
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)