Problem 16 Find the value of each of the fo... [FREE SOLUTION]

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Chapter 10: Problem 16

Find the value of each of the following. Use a calculator to check each result. $$ (-3)(-9) $$

Short Answer

Expert verified

The product of $(-3)$ and $(-9)$ is 27.

Step by step solution

Understand the Problem

We need to find the product of two negative numbers, specifically $(-3)$ and $(-9)$. This involves multiplication.

Recall the Rule for Multiplying Negatives

When multiplying two negative numbers, the product is positive. Therefore, $(-3) \times (-9)$ will have a positive result.

Multiply the Absolute Values

Ignore the negative signs temporarily and multiply the absolute values: \[3 \times 9 = 27\]

Apply the Sign Rule

Since multiplying two negative numbers gives a positive result, the product of $(-3)$ and $(-9)$ is \[+27\].

Verify with a Calculator

Use a calculator to check: Enter $(-3)$ multiplied by $(-9)$. The result should show as 27. This confirms our solution.

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Key Concepts

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

Rule for Multiplying Negatives

When we talk about multiplying negative numbers, there's a simple rule to remember: **The product of two negative numbers is positive.** This might seem strange at first, but it's a key rule in math.

Think of it like walking backwards on a number line. If you "go backward" (multiply by a negative) twice, you end up going forward. This is why multiplying $-(3)$ and $-(9)$ results in a positive number. The negative signs effectively cancel each other out.

*Negative times negative equals positive*
Effects like reversing a backward motion.
Helps in understanding how numbers behave differently under multiplication.

Absolute Value Multiplication

In mathematics, absolute value refers to the distance of a number from zero on a number line, regardless of its direction (positive or negative). When multiplying, focusing on absolute values can simplify the problem.

To solve $(-3) \times (-9)$, ignore the negative signs initially and multiply the absolute values: \3 \times 9 = 27\. Once you've multiplied the absolute values, simply apply the rule we discussed: multiply the sign back in. Here, two negatives make a positive, so the final answer is \[+27\].

This technique helps to:

Keep calculations straightforward and simple.
Avoid confusion with negative signs during multiplication.
Ensure correctness by breaking down complex steps.

Calculator Verification

After thinking through the rules and performing manual calculations, it is always a good idea to verify your results. A calculator is a handy tool for this. To check the product of $-3) \times (-9)$, enter it into a calculator.

By doing this, you confirm the answer is indeed \27\. If the calculator shows a different result, it's an indicator to recheck your understanding of negative multiplication rules and absolute values.

Regular calculator verification can:

Provide confidence in accuracy.
Help recognize and catch potential errors.
Serve as a learning tool to reinforce math concepts.

Always remember, technology is there to support our mathematical journey, ensuring confidence and understanding in problem-solving.

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91影视

Find the value of each of the following. Use a calculator to check each result. $$ (-3)(-9) $$

Short Answer

Step by step solution

Understand the Problem

Recall the Rule for Multiplying Negatives

Multiply the Absolute Values

Apply the Sign Rule

Verify with a Calculator

Key Concepts

Rule for Multiplying Negatives

Absolute Value Multiplication

Calculator Verification

One App. One Place for Learning.

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