The same rules hold true for multiplication. When you divide two negative numbers then the quotient is positive. When you divide a positive number by a negative number then the quotient is also negative. When you divide a negative number by a positive number then the quotient is negative. So, the quotient of a negative and a positive number is negative and, correspondingly, the quotient of a positive and a negative number is also negative. What happens when you divide two negative numbers? For example,įor the denominator (-3) to become the numerator (-12), you would have to multiply it by 4, therefore the quotient is 4. In order to check whether 4 is the correct answer, we multiply 3 (the denominator) by 4 (the quotient): If you answer is correct then the product of these two numbers should be the same as the numerator. Turning to division, you may recall that you can confirm the answer you get by multiplying the quotient by the denominator. This switch removes the doublenegative sign, which has been noted to be particularly difficult for both children and adults Kilhamn, 2004 Vlassis, 2004, and leaves a simplified addition problem. Now we have two negative numbers, so the result is positive. A major strategy for solving negative subtraction problems is to translate them into addition, changing minus a negative into plus a positive. Since there is one positive and one negative number, the product is negative 12. ![]() When we add a negative integer, the given number’s value decreases. The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that. In the case of integers, however, an addition operation might result in an increase or decrease in the value of the given number. Why negative plus negative equals positive Each number has an additive inverse associated to it (a sort of opposite number), which when added to the original number gives zero. In general, addition means to increase the value. ![]() Two quick multiplication examples:ģ times 4 equals 12. Solution: There are different rules of adding negative numbers. In multiplication and division, however, you calculate the result as if there were no minus signs and then look at the signs to determine whether your result is positive or negative. This is similar to the rule for adding and subtracting: two minus signs become a plus, while a plus and a minus become a minus. When you multiply two negative numbers or two positive numbers then the product is always positive. When you multiply a negative number by a positive number then the product is always negative. You also have to pay attention to the signs when you multiply and divide.
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