Problem 13 - Prealgebra

Question

Find each of the following quotients. (Divide.) [Examples 1–5] $$\frac{0}{-3}$$

Step-by-Step Solution

Answer

The quotient is 0.

Step 1: Understand Division by a Negative Number

When dividing zero by any non-zero number, whether positive or negative, the quotient is zero. This is because zero divided by any quantity results in zero. In this problem, we are dividing zero by -3.

Step 2: Apply the Rule

According to the division rule for zero, if a number is divided by a non-zero number, the result is zero. Hence, \( \frac{0}{-3} = 0 \). The sign of the divisor does not affect the outcome when dividing zero.

Key Concepts

Zero Divided by Negative

When dealing with division problems, one important concept is dividing zero by a negative number. This concept can be a bit confusing at first, but it's simpler than it seems. If you divide zero by any non-zero number, the result is always zero. It doesn't matter if the number is negative or positive. The key here is that zero divided by anything cannot have any parts in the dividend since there are no parts to divide.
So, in the case of the exercise where we divide zero by (-3), we end up with zero. The negative sign of -3 does not alter the result of the division because the concept of dividing zero underlines that there are no quantities being shared or distributed.

Division Rules

Understanding division involves knowing some basic rules. These rules clarify how division works across different scenarios, especially involving zero:

• When zero is in the numerator (top number), the result of the division is zero, as long as the denominator (bottom number) is not zero.
• If zero is in the denominator, division is undefined because you cannot divide by zero.
• When dividing by a negative number, the sign of the quotient typically changes except when zero is divided.

It is good to remember these rules to avoid mistakes in arithmetic operations. This understanding makes solving division problems like the given one a lot easier.

Quotient Definition

The term "quotient" is essential when discussing division. A quotient is the result you get after dividing one number by another. For example, in dividing 0 by -3, the quotient is 0. This is because zero remains zero no matter how it's divided, as long as it's a non-zero division.
The formula for calculating a quotient is simple: it is simply the dividend (the number being divided) divided by the divisor (the number you are dividing by). A crucial point to note about quotients is that they tell us how many times a divisor can fit into the dividend.
In scenarios where the dividend is zero, such as in our exercise, the divisor sees zero fitting into it no times, hence a quotient of zero.