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Chapter 2: Problem 24

Write as an equivalent addition; then evaluate. $$0-6$$

Short Answer

Expert verified
Answer: The equivalent addition expression for 0 - 6 is 0 + (-6) and its value is -6.

Step by step solution

01

Identify the Inverse

To rewrite 0 - 6 as an addition problem, we must find the inverse of 6. The inverse of a number is the number added to it to get 0 as the sum. In this case, the inverse of 6 is -6.
02

Rewrite as Addition

Now that we have identified the inverse, we can rewrite the original subtraction problem as an equivalent addition problem. Remember that the original problem is 0 - 6. To rewrite it as an addition problem, replace the subtraction symbol with the addition symbol and use the inverse of 6: $$0 + (-6)$$
03

Evaluate the Expression

Now we can evaluate the equivalent addition expression that we just rewrote: $$0 + (-6) = -6$$ So, the result of the expression is -6.

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Key Concepts

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

Inverse in Math
In mathematics, the concept of an inverse is fundamental. It involves finding a number that when added to the original number results in zero. This is particularly useful in transforming subtraction problems into addition problems.

For example, in the expression \(0 - 6\), we need to transform the subtraction into an addition. We do this by finding the inverse of 6, which is -6. Why? Because \(6 + (-6) = 0\). The inverse changes subtraction into something easier to handle, especially when dealing with negative numbers. The idea of inverse helps simplify calculations and improve understanding of mathematical expressions.
Integer Addition
Adding integers might seem straightforward, but it's crucial in solving more complex equations. Integers include positive, negative numbers, and zero. When performing addition with integers, remember these points:
  • Adding two positive integers results in a more significant positive integer.
  • Adding two negative integers gives a bigger negative integer.
  • Adding a positive and a negative integer involves finding the difference between their absolute values. The sign of the result will be that of the larger absolute value.
In our example, \(0 + (-6)\), we are essentially just adding a negative integer to zero. This means we move 6 units in the negative direction from zero, resulting in -6.
Mathematical Expressions Evaluation
Evaluating mathematical expressions involves simplifying or solving to find a result. When transforming subtraction into addition, it is crucial to follow accurate steps to ensure the correct answer.

Let's take the expression \(0 - 6\) and convert it to an addition problem: \(0 + (-6)\). By simply understanding that subtracting is the same as adding the inverse, we evaluate by following clear steps:
  • Identify the original operation: subtraction.
  • Find the inverse of the number being subtracted: -6.
  • Rewrite the expression as an addition problem: \(0 + (-6)\).
  • Solve the addition problem to get the result: -6.
Following these steps makes evaluating expressions simple and straightforward.

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