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If the divide and the minus signs are interchanged and the numbers 8 and 4 are interchanged, then which of the following equations will become true.

Question

If the divide and the minus signs are interchanged and the numbers 8 and 4 are interchanged, then which of the following equations will become true.

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Solution

To solve this problem, we need to analyze the situation carefully. Let's break it down step by step.

1. Break Down the Problem

Given two numbers, 8 and 4, we are to interchange the division (÷) and subtraction (−) signs, as well as the two numbers.

2. Relevant Concepts

Let's consider the basic operations involved:

  • The original operation could be either 84 8 - 4 or 8÷4 8 \div 4 .
  • After interchanging, the operations will become 4÷8 4 \div 8 or 48 4 - 8 .

3. Analysis and Detail

Let's evaluate both possibilities:

  1. Original Expression: 84 8 - 4

    • Calculation: 84=4 8 - 4 = 4
    • Interchanged Expression: 4÷8=0.5 4 \div 8 = 0.5
  2. Original Expression: 8÷4 8 \div 4

    • Calculation: 8÷4=2 8 \div 4 = 2
    • Interchanged Expression: 48=4 4 - 8 = -4

4. Verify and Summarize

We analyzed both potential original equations and their transformed versions.

  1. From 84=4 8 - 4 = 4 to 4÷8=0.5 4 \div 8 = 0.5
  2. From 8÷4=2 8 \div 4 = 2 to 48=4 4 - 8 = -4

Neither transformation results in a true equation.

Final Answer

No equation becomes true with the given transformations.

This problem has been solved

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