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Chapter 1: Problem 47

Find each quotient. $$ \frac{0}{-5} $$

Short Answer

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Step by step solution

01

Understand the problem

The problem asks to find the quotient of 0 divided by -5. The division of a number by another number results in the quotient.
02

Recall the division rules involving zero

Remember that any number divided by another non-zero number yields zero.
03

Apply the division rule

Since zero divided by any non-zero number is zero, we apply this rule here. Therefore, \( \frac{0}{-5} = 0 \).

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Key Concepts

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

quotient
In algebra, when you divide one number by another, the result is called the quotient. It's a fundamental concept. The quotient can be found by simply performing division. For example, in the exercise given, \( \frac{0}{-5} \) asks us to find the quotient when 0 is divided by -5. Remember: dividing 0 by any number (except zero) results in 0. So, the quotient here is 0.
division rules
Knowing the division rules can simplify complex problems. Here are some key rules:
  • Any number divided by 1 remains the same.
  • Dividing by zero is undefined. You cannot divide a number by zero.
  • Zero divided by any non-zero number is always zero.
In the exercise, we see \( \frac{0}{-5} \) uses the rule that zero divided by any non-zero number equals zero. Applying this rule confirms that the answer is 0.
zero properties
Zero has unique properties in algebra. Understanding these can help in various mathematical problems.
  • If you add zero to any number, the number remains unchanged.
  • Multiplying any number by zero gives zero.
  • Zero divided by any non-zero number is zero.
  • However, division by zero is undefined and cannot be performed.
In the given problem, we used the property that says \( \frac{0}{\text{anything}} = 0 \). This property helped us see that \( \frac{0}{-5} = 0 \).
basic algebra
Basic algebra introduces fundamental operations like addition, subtraction, multiplication, and division. These operations apply rules, such as how zero behaves during division. Division itself is distributing a number into equal parts. Knowing key concepts:
  • Quotient: The result of division.
  • Division by zero is undefined.
  • Dividing zero by any number equals zero.
This problem, \( \frac{0}{-5} = 0 \), is a straightforward example showing basic algebra's simplicity. Understanding these basics ensures a strong mathematical foundation.

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Most popular questions from this chapter

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(23,18,13,-4,\) and \(-8\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ \left(\frac{1}{3} x-\frac{4}{5} y\right)\left(-\frac{1}{5} a\right) $$

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Five times a number, added to the sum of the number and three

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(18,12,0,-4,\) and \(-10\)

Simplify each expression. $$ 1+7 x+11 x-1+5 x $$
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