why (-4)x(-2)=8?

Question

Why the multiplication of negative number with another negative number is positive number

Answer 1

To get to the root of this question, we have to understand what negative numbers really “mean”. Let’s pretend someone loans you $4 and you go and spend it right away. How much money do you have? You can say, “I have no money, and I also owe $4”. Mathematically in this situation, you can also say, “I have –$4.” If you borrowed $4 from two different people, you can say, “I have -$4 x 2 loans, or –$8”.

Since we have defined a loan in which you borrowed money as positive, it is reasonable to define a “negative loan” as one in which you loaned the money to someone else. If you loan $4 to someone else, that’s $4 you don’t have anymore, so you can call it -$4. But if you make two “negative loans” then (-$4) x (-2 loans) = $8. So, on paper, you have $8, since assuming the loans will be paid back, you have assets of $8. So a negative times a negative resulting in a positive makes perfect sense.

Answer 2

I don't know why, but that's how it is. Everyone here, all around the world, learned it this way. It's just something you have to remember. Two negatives make a positive and a positive times a negative makes a negative.

Answer 3

The product of two same number sign is always give positive value and different sign values gives negative value,
Therefore,

(-4) x (-2) = 8

Answer 4

4 x 2 = 8
-4 x 2 = -8
therefore -4 x -2 = 8
the 2 negative signs can be cancelled out

Answer 5

see there are certain rules to be followed that have been already set up by the people who found all these relations or equations of mathematics.

now if u say that why do call a pencil with that word and not others.
than there is no answer or solution to it,so we no other choice but to accept it.

in the similar manner we have to accept that multiplication of two negative digits turns out to be a positive one.

but still i give u a detailed solutuion of it:::::::::::::::;;
Why is −1 multiplied by −1 equal to 1? More generally, why is a negative times a negative a positive? There are two ways to answer this question. The first is intuitive and conceptual; the second is formal and algebraic.


Intuitive explanation
There are many ways to conceptualise multiplication. Let's confine ourselves to positive numbers, for the moment.

Now, multiplication is basically repeated addition. To multiply 5 by 3, we can imagine a straight stick 5 metres long in front of us. We lay it out flat 3 times in the same direction, with the back tip of the stick placed where the front tip was on the previous time. After we lay it down 3 times, the front tip will lie exactly 5 × 3 = 15 metres from the back tip where we originally placed it.

What would it mean to lay down a stick "negatively many times"? One answer is to say that it would result in a displacement where, if we were to lay it down 3 times immediately after, we would return to where we started. Imagine performing this. It is the same action as multiplying by a positive number except we are pointing in the opposite direction. If we were going east to multiply by a positive, we go west to multiply by a negative.

This is fine, but it only covers a stick of "positive length". How do we multiply using this type of stick? If we assume that multiplication should not depend on order, then 5 × −3 = −3 × 5 = − 15. Now, stand at a point. Laying out a stick of length 5, minus 3 times, sends us 15 metres west (using the east/west above). However, this is the same result as if we had pointed west originally and laid a stick of 5 metres down 3 times. In other words, to multiply using a stick of negative length, we should point ourselves in the opposite direction before laying down the stick.

Now, we can see why −1 × −1 = 1. We point east originally. Our stick has length −1, so we turn ourselves to point west. Then, we lay the stick down negative one times, i.e. we point ourselves back again in the east direction and lay the stick down. This is the same as if we had simply dropped the stick in front of us pointing east without moving ourselves at all.


Algebraic explanation
The algebraic explanation is essentially a formalisation of the above intuitive explanation. Start with the equation


The first equality follows from the fact that "anything times zero is zero". The second follows from the definition of −1 as additive inverse of 1: it is precisely that number that when added to 1 gives 0. Now, using the distributive law, we see that


The second equality follows from the fact that 1 is a multiplicative identity and simple addition. But now we add 1 to both sides of this last equation to see that

−1 × −1 = 1.
The above argument holds in any ring. It has a flavour common to some of the basic results in abstract algebra.


Computer representation
There are a variety of ways that −1 (and negative numbers in general) can be represented in computer systems, the most common being as two's complement of their positive form. Since this representation could also represent a positive integer in standard binary representation, a programmer must be careful not to confuse the two. Negative one in two's complement could be mistaken for the positive integer 2n − 1, where n is the number of digits in the representation (that is, the number of bits in the data type). For example, 111111112 (binary) and FF16 (hex) each represents −1 in two's complement, but represents 255 in standard numeric representation

Answer 6

Think of it like this

-4 * 2 would = -8, becuase you have two lots of -4.

So -4 * -2 would have to be positive as you can't have the same answer.

Answer 7

-4*-2=
-(-2+-2+-2+-2) = -(-8) or 8
one way to read negative signs is to say the opposite of,
so, it reduces to the opposite of the opposite of 8,

Answer 8

negative number multified by another negative number will givepositive result

Answer 9

Because 0=(-4 + 4)*(2) = -4*2 + 4*2 = -4*2 + 8 // Subtracting 8 from both sides we get:
(*) -8 = -4*2

Now, 0=-4*(-2 + 2) = -4*(-2) + (-4)*2 = -4*(-2) - 8 ; (adding the -8 from (*))

Now add 8 to both sides and get

8=(-4)*(-2)

Answer 10

-*-=+ SO,(-4)*(-2)=8.