Demystifying Division- Unraveling the Mystery of Negative Numbers Divided by Negative Numbers

What is a negative number divided by a negative number? This question might seem simple at first glance, but it actually delves into the fascinating world of mathematics, specifically the rules of division with negative numbers. Understanding this concept is crucial for anyone studying algebra or pursuing a career in the field of mathematics.

In mathematics, division is defined as the inverse operation of multiplication. When we divide a number by another number, we are essentially asking how many times the divisor can be subtracted from the dividend to obtain a result of zero. When dealing with negative numbers, the rules of division become slightly more complex, but they are still consistent and predictable.

To answer the question, “What is a negative number divided by a negative number?” let’s consider a simple example. Suppose we have the expression (-6) divided by (-2). To solve this, we can think of it as asking how many times -2 can be subtracted from -6 to get zero. Since -2 is a negative number, subtracting it from -6 will result in a smaller negative number. In this case, -2 can be subtracted three times from -6, as follows:

(-6) – (-2) = -6 + 2 = -4
(-4) – (-2) = -4 + 2 = -2
(-2) – (-2) = -2 + 2 = 0

As we can see, -2 can be subtracted three times from -6 to get zero. Therefore, (-6) divided by (-2) equals 3.

The rule for dividing two negative numbers is that the result will always be a positive number. This is because when you divide two negative numbers, you are essentially multiplying a positive number by a positive number. For instance, (-6) divided by (-2) is the same as (-6) multiplied by (-1/2), which is 3.

In conclusion, when faced with the question, “What is a negative number divided by a negative number?” the answer is always a positive number. This rule is a fundamental concept in mathematics and is essential for understanding more complex algebraic expressions and equations. By mastering this concept, you will be well on your way to becoming a proficient mathematician.