Really? I didn't have any trouble finding this:
Why do we get a positive number when we multiply two negative numbers?
When we multiply or divide two negative numbers, the result is a positive number. This might seem strange at first, but it's important to remember that a negative sign in math is really just an instruction to change the direction of a number on a number line. So when we multiply or divide two negative numbers, we're reversing the direction twice, which brings us back to a positive number.
But I have a trouble in finding here is how
Negative sign on a number line tells us to go in negative direction while positive sign tells us to go in positive direction.
The sum of +3 and -8 is -5.
On a number line, count 3 in a positive direction from zero. At the same point, count 8 but in negative direction (opposite to positive) till we reach to the point of -5. OR
On the same number line, count 8 in a negative direction from zero. At the same point, count 3 but in positive direction (opposite to negative) till we reach at the point of -5
So the REVERSE (opposite) of NEGATIVE is POSITIVE and vice versa.
Multiplication reduced the laborious work of addition / subtraction
For example
The product of +3 and +5 means
The sum of +3 five times in the direction positive sign = +3 + 3 + 3 + 3 + 3 = +15 or the sum of +5 three times in positive direction = +5 + 5 + 5 = +15
No negative sign is seen which tells to go in opposite direction in the above example therefore the answer is a positive number
Similarly, the product of - 3 and -5 must also means
The sum of - 3 five times in the direction of negative sign = - 3 - 3 - 3 - 3 - 3 = -15 or the sum of -5 three times in negative direction = -5 - 5 - 5 = -15
No positive sign is seen which guide us to go in REVERSE/positive direction in the product of two negative numbers.
This means if + x + = +, then – x - must also = - , but, not