Mathematical operations with zero are often allocated with special rules and even the bans. So, all school students from elementary school acquire the rule: "It is impossible to divide into zero". It is even more rather negative numbers of rules and conventions. All this considerably complicates understanding by the school student of material so sometimes it is even unclear whether it is possible to divide zero into a negative number.

## What is the division

First of all, whether it is possible to understand zero to divide into a negative number, it is necessary to remember how in general division of negative numbers is carried out. Mathematical operation of division represents action, the return to multiplication.

It can be described as follows: if an and b rational numbers then to divide an into b, it means to find such number with which at multiplication by b will give as a result number a. This definition of division is right both for positive, and for negative numbers if dividers are other than zero. At the same time the condition is strictly met that it is impossible to divide into zero.

Therefore, for example, to divide number 32 into number-8, it is necessary to find such number which at multiplication by number-8 will give as a result number 32. Such number will be-4 as

(-4) x (-8) = 32. Signs at the same time develop, and minus on minus will give as a result plus.

Thus:

32: (-8) =-3.

Other examples of division of rational numbers:

21: 7 = 3, as 7 x 3 = 21,

(−9): (−3) = 3, as 3 · (−3) = −9.

## Rules of division of negative numbers

To define the module of private, it is necessary to divide the module of divisible number into the divider module. At the same time it is important to consider the sign and that, and other element of operation.

To divide two numbers with identical signs, it is necessary to divide the module of a dividend into the divider module, and before result to put a plus.

To divide two numbers with different signs, it is necessary to divide the module of a dividend into the divider module, but before result to put a minus sign, and it is unimportant what of elements, a divider or a dividend, was negative.

The specified rules and ratios between results of multiplication and division, known for positive numbers, are fair also for all rational numbers, except number zero.

For zero there is an important rule: private from division of zero into any number, other than zero, it is also equal to zero.

0: b = 0, b ≠ 0. And b can be both a positive, and negative number.

Thus, it is possible to draw a conclusion that zero can be divided into a negative number, and as a result there will always be zero.