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A very way to understand this very logically.

First know what is multiplication?

It is recurring addition.

So if we multiply 3 by (-2), that means:-

(-2)+(-2)+(-2)= -6

Now see the examples below:

4 X (-4) = -16

3 X (-4) = -12

2 X (-4) = -8

1 X (-4) = -4

0 X (-4) = 0

Have you noticed a trend. Notice carefully that as the numbers which are being multiplied by (-4) are decreasing 1 by 1 the product is increasing by (+4).

So for the numbers 4,3,2,1,0 the products are:-

-16

-16+4= -12

-12+4= -8

-8+4= -4

-4+4=0

So what will be in the next step when we do:

(-1) X (-4)=?

The series will continue 0+4 an will result to a positive 4

and it will go like this:

(-1) X (-4)= 4

(-2) X (-4)= 8

(-3) X (-4)= 12

+4 is added in each step. This was the best explanation to this according to me which was told to me by my teacher which he made himself.

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Q: Why is the product of two negative integers a positive integer?
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Related questions

The product of any two integers is a positive integer?

No, if a negative integer is multiplied by a positive integer, the product is negative. However, if both of the integers are either positive or negative, the product is positive.


What can you say about the product of an integer and a positive integer?

-- The product is an integer. -- If the original two integers are both positive, then the product is positive. -- If the original two integers have different signs, then the product is negative.


What is the product of a positive integers and negative integer?

always a negative


What is the product of two negative integers?

The product of two negative integers is positive as for example -4 times -5 = 20


What is the product of an even number of negative integers?

A positive integer.


Are the sum of two negative integers positive?

No. Two negative integers added together will never equal a positive integer. It is the product of two negative integers that is positive.


What is the rule in dividing integers?

The rule in dividing integers is to divide the absolute values. Two positive integers or two negative integers equals positive product. If one integer is positive and the other is negative, the product is negative.


What is the product of 5 negative integers and 1 positive integer?

Negative 4


Is the product of a negative and positive integer a negative?

Yes. The product of a negative integer and a positive integer is a negative integer.


What is the rules for multiplication integers?

When multiplying integers, multiplying by the same sign will always produce a positive integer. Such as a negative times a negative equals a positive. If the signs are different then the product will be a negative.


Is the product of 4 negative integers positive or negative?

Positive. The product of even numbers of negative integers is always positive, whereas the product of odd nummbers of negative integers is always negative.


What is the product of positive integer and negative integer?

negative