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Chapter 3: Problem 25

Fill in the blank with the appropriate number. $$_____ +(-7)=0$$

Short Answer

Expert verified
The number is 7.

Step by step solution

01

Understand the Equation

The equation that needs to be solved is \( \_ + (-7) = 0 \). The goal is to find the number that, when added to -7, equals 0.
02

Determine the Inverse Operation

To isolate the blank, consider the inverse of adding -7. The inverse operation is adding 7.
03

Solve for the Blank

If adding -7 to a number results in 0, adding 7 to both sides will isolate the blank. Therefore, we write: \( \_ + (-7) + 7 = 0 + 7 \). Simplifying this leads to \( \_ = 7 \).

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Key Concepts

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

Inverse Operations
Inverse operations are essential concepts when solving equations. They allow us to reverse the effects of an operation, helping to isolate variables or unknowns. For example, addition and subtraction are inverse operations because they undo each other. Likewise, multiplication and division are inverses of each other too. When you see the term 'inverse operation,' think about the opposite action that can counterbalance the given one. In this exercise, the equation is \(_ + (-7) = 0\). To isolate the blank, we need the inverse of adding -7. The inverse of adding -7 is adding 7. By using inverse operations, we can effectively solve the equation and find the missing number.
Addition
Addition is the process of combining two or more numbers to get a total. It鈥檚 one of the basic arithmetic operations and is fundamental in mathematics. In the context of the exercise, understanding addition helps us solve the equation. Here, we have \(_ + (-7) = 0\). Think of what number added to -7 gives a sum of zero. In other words, we're looking for a number that, when combined with -7, results in no change. The answer is 7 because \[7 + (-7) = 0\].Being familiar with addition and how it works with negative numbers helps you quickly solve similar problems.
Zero Property
The zero property of addition states that any number plus zero is the original number. However, when dealing with an equation that sums to zero, like \(_ + (-7) = 0\), it鈥檚 slightly different. You're looking for the value that, when added to -7, results in zero. This property can help simplify many algebraic problems. In this scenario, if adding -7 leads to zero, it tells us that the missing number must balance out the -7, making the integer value positive 7. Thus, knowing the zero property gives you the insight to deduce that \(7 + (-7) = 0\) and successfully solve the equation.

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