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Chapter 2: Problem 14

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

Short Answer

Expert verified
The quotient is 0.

Step by step solution

01

Interpreting the Problem

The problem asks us to divide 0 by -5. We can think of this as asking how many times -5 can fit into 0, or what is the value of zero divided by a negative number.
02

Applying Division Rules

According to basic division rules, any number divided by zero results in zero. This is because zero pieces cannot fit even once into any number, positive or negative.
03

Final Calculation

Based on the division rules, we see that \( \frac{0}{-5} = 0 \), meaning zero divided by any nonzero number is zero.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Basic Division Rules
Division is one of the fundamental operations in mathematics. It involves determining how many times one number, called the divisor, fits into another number, known as the dividend. Here are a few key points about division:
  • The basic formula for division is: Dividend 梅 Divisor = Quotient.
  • Division is essentially the opposite of multiplication. If you multiply the quotient by the divisor, you'll get back the original dividend.
  • Division by zero is undefined because no number of "zeros" can fit into any number.
It's crucial to understand these simple rules as they form the foundation for more advanced mathematical concepts. When dealing with zero as either the dividend or the divisor, special rules apply which we will explore further.
Zero Property of Division
The zero property of division specifically addresses scenarios where zero is involved in a division problem, either as the dividend or divisor:
  • If 0 is the dividend (the number being divided), the result is always 0, provided the divisor is not zero. For example, \( \frac{0}{5} = 0 \).
  • Zero cannot be the divisor. If you try to divide any number by zero, the division is undefined. This is because you cannot determine how many times zero goes into another number since zero has no value or size.
Understanding the zero property helps avoid common mistakes, especially in algebra and calculus. Knowing that \( \frac{0}{a} = 0 \) where \( a eq 0 \) simplifies many mathematical problems.
Dividing by Negative Numbers
When dividing by negative numbers, it is important to understand how the sign affects the quotient. Here are the rules:
  • Dividing a positive number by a negative number results in a negative quotient. For instance, \( \frac{5}{-1} = -5 \).
  • Similarly, dividing a negative number by a positive number also yields a negative quotient. Example: \( \frac{-10}{2} = -5 \).
  • When both dividend and divisor are negative, the quotient is positive. For example, \( \frac{-6}{-2} = 3 \).
This understanding is key in algebra where equations may include unknowns with negative values. The rules governing negative division help maintain consistency and accuracy in calculations.

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Most popular questions from this chapter

Simplify as much as possible by first changing all subtractions to addition of the opposite and then adding left to right. $$12-30-47$$

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Rewrite the following using the commutative property of multiplication. $$7(x)=$$

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