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Chapter 2: Problem 77

Simplify each given expression. \(0 \div 5\)

Short Answer

Expert verified
The simplified expression is 0.

Step by step solution

01

Identify the Operation

The expression given is a division problem: \(0 \div 5\). This involves dividing zero by five.
02

Understand Division with Zero

In division, when zero is divided by any non-zero number, the result is always zero. This is because zero represents nothing and dividing nothing among any number of groups still results in nothing per group.
03

Perform the Calculation

Based on the rule from Step 2, apply the division: \(0 \div 5 = 0\). This expresses that zero divided equally into any number of parts is zero.

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Key Concepts

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

Division by Zero
Division is an arithmetic operation, much like addition, subtraction, or multiplication. However, division has specific rules, especially when it comes to zero. Understanding these rules is crucial. When we say division by zero, we usually mean dividing a number by zero, represented as \(a \div 0\). But, what happens when we try to divide by zero? Well, it turns into a problem as the result is undefined. Simply put:
  • Any number divided by zero does not have a valid numerical value.
  • This is because dividing by zero doesn't fit the basic logic of arithmetic operations.
In simpler terms, since you cannot split something into zero parts, division by zero leads to an undefined situation. So, always remember to avoid dividing any number by zero in mathematics!
Arithmetic Operations
Arithmetic operations are basic mathematical operations used all around us. They include addition, subtraction, multiplication, and division. Each operation follows its rules, and it's vital to understand them for problem-solving. Here's a quick rundown of what they entail:
  • Addition: Combining numbers to get a total. For example, \(3 + 2 = 5\).
  • Subtraction: Taking away one number from another. For example, \(5 - 2 = 3\).
  • Multiplication: Repeated addition of the same number. For example, \(3 \times 2 = 6\).
  • Division: Splitting a number into equal parts. For example, \(6 \div 2 = 3\).
Each operation has its function, and knowledge of their basics helps us solve diverse mathematical problems. Division is unique because of the specific scenarios like division by zero which we must handle with care.
Properties of Zero
Zero is a fascinating number with unique properties that affect arithmetic operations in interesting ways, especially in division. Here are some significant properties you should know:
  • Additive Identity: Adding zero to any number doesn't change its value. For instance, \(a + 0 = a\).
  • Multiplicative Property: Any number multiplied by zero results in zero, like \(a \times 0 = 0\).
  • Division: Zero divided by any non-zero number is zero. As in the exercise where \(0 \div 5 = 0\).
  • Undefined Division: Dividing a non-zero number by zero is undefined, showcasing the unique nature of zero in operations.
These properties illustrate the central role zero plays in arithmetic and help to simplify complex expressions by understanding how zero interacts with other numbers.

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Most popular questions from this chapter

Compute the exact value of the given expression. \(9+16 \div 2 \cdot 4-9\)

Provide a number line sketch with your answer. What number lies two units to the right of \(-5\) on the number line?

State the property of addition depicted by the given identity. \(17+(-2)=-2+17\)

Find the sum of the given integers. \(11+(-16)+16\)

Find the difference. \(10-12\)
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