Problem 586 Multiply. $$ (-9.16)(-68.34)... [FREE SOLUTION]

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Chapter 1: Problem 586

Multiply. $$ (-9.16)(-68.34) $$

Short Answer

Expert verified

+626.0544

Step by step solution

Understand the signs

Both numbers are negative. When two negative numbers are multiplied, the result is positive.

Multiply the absolute values

Ignore the negative signs and multiply the absolute values: $-9.16 \times -68.34 = 9.16 \times 68.34$

Perform the multiplication

Multiply the absolute values of the numbers: $9.16 \times 68.34 = 626.0544$

Apply the sign

Since the product of two negative numbers is positive, the result is $+626.0544$. So the final answer is $+626.0544$.

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Key Concepts

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

Multiplying Negative Numbers

Multiplying negative numbers can seem tricky at first. But the rule is simple: when you multiply two negative numbers, the result will always be positive. Here's why: Imagine you owe someone money (which is negative) and you double your debt (multiplying by another negative). In a sense, you remove that negativity by doubling it, turning the result positive.
Whenever faced with negative numbers, remember this key rule: negative times negative equals positive.
In our example, both $ -9.16 $ and $-68.34$ are negative. Multiplying them gives a positive result.

Absolute Value Multiplication

To make multiplication simpler, we can use the concept of absolute values. The absolute value of a number is its distance from 0 without considering its sign. It's always non-negative.
For example, the absolute value of $-9.16$ is $9.16$ and the absolute value of $-68.34$ is $68.34$.

When you multiply negative numbers, it's helpful to ignore the signs initially and just multiply these absolute values.
In our exercise, we first ignore the negative signs:
Multiplying $9.16 $ by $68.34$:

\[ 9.16 \times 68.34 = 626.0544 \]

This simplifies the calculation process, enabling you to focus on getting the multiplication right.

Positive Result from Negative Product

Now let's make sense of the final result. We know that multiplying two negative numbers gives a positive product. Although we used absolute values for the multiplication, the end result must reflect the actual signs of the numbers we started with.
Thus, $-9.16 \times -68.34$ yields a positive product.

This occurs because multiplying negatives 'inverts' the signs: - times - becomes +.
That's why from our exercise, $ -9.16 \times -68.34 = 626.0544$.

So, remember: When dealing with negative numbers in multiplication, always take into consideration the property that makes their product positive.
It's a crucial step to ensure you get the right answer.

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91影视

Multiply. $$ (-9.16)(-68.34) $$

Short Answer

Step by step solution

Understand the signs

Multiply the absolute values

Perform the multiplication

Apply the sign

Key Concepts

Multiplying Negative Numbers

Absolute Value Multiplication

Positive Result from Negative Product

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