Problem 88 Evaluate the expressions for the... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 2: Problem 88

Evaluate the expressions for the given values of the variables. $$n^{2} \text { for } n=-9$$

Short Answer

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Step by step solution

Identify the Given Expression

The given expression is: \[ n^{2} \] where $ n = -9 $.

Substitute the Given Value

Replace $ n $ with -9 in the expression. This gives us: \[ (-9)^{2} \]

Calculate the Square

Square the value -9. Remember, squaring a negative number results in a positive number: \[ (-9)^{2} = 81 \]

Conclusion

Therefore, the value of the expression $ n^{2} $ when $ n = -9 $ is: \[ 81 \]

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Key Concepts

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

Substitution in Algebra

In algebra, substitution involves replacing variables in an expression with specific values. This helps in evaluating the expression for particular situations.

Let's break it down:

Identify the variable in the expression. In our problem, the variable is $ n $.
Replace, or substitute, the variable with its given value. Here, $ n $ is substituted with -9.

Substitution is crucial as it simplifies expressions and helps us solve for specific values. Whenever you see a variable, just plug in the given number and follow the next steps carefully.

Squaring Numbers

Squaring a number means multiplying it by itself. You may see it represented by an exponent of 2. For example, $ n^{2} $ means $ n \times n $.

Here's what essentially happens when we square a number:

For any number $ k $, squaring it gives $ k \times k $.
In our problem, we had $ n = -9 $, so we calculated $ (-9)^{2} $.

聽 Squaring is a straightforward but powerful operation, turning both negative and positive numbers into positive results. It's important to carefully follow through with calculations to avoid common pitfalls.

Negative Numbers

Negative numbers can sometimes be tricky but understanding them is vital. When we multiply two negative numbers, the result is positive.

In our case with $ (-9)^{2} $:

Think of it as $ -9 \times -9 $.
As both numbers are negative, their multiplication results in a positive product: $ (-9) \times (-9) = 81 $.

This principle always holds true for any pair of negative numbers. Remembering that two negatives make a positive can prevent errors in calculations.

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91影视

Evaluate the expressions for the given values of the variables. $$n^{2} \text { for } n=-9$$

Short Answer

Step by step solution

Identify the Given Expression

Substitute the Given Value

Calculate the Square

Conclusion

Key Concepts

Substitution in Algebra

Squaring Numbers

Negative Numbers

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