Problem 75 Find each product. $$ -10\le... [FREE SOLUTION]

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Chapter 0: Problem 75

Find each product. $$ -10\left(-\frac{1}{5}\right) $$

Short Answer

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Step by step solution

Understand the problem

You need to find the product of $-10$ and $-\frac{1}{5}$.

Multiply the numbers

First, multiply the absolute values: \[10 \times \frac{1}{5} = 2\].

Determine the sign

Both $-10$ and $-\frac{1}{5}$ are negative. The product of two negative numbers is positive, so the result is $2$.

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Key Concepts

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

Absolute Values

Absolute values represent the distance of a number from zero, regardless of its sign. This means both positive and negative numbers have positive absolute values. For instance, the absolute value of $-10$ is $|-10| = 10$, and the absolute value of $-\frac{1}{5}$ is $|-\frac{1}{5}| = \frac{1}{5}$.

When multiplying numbers, focusing on their absolute values first simplifies the process. For example, to multiply $-10$ and $-\frac{1}{5}$, you first calculate the product of their absolute values: $10 \times \frac{1}{5} = 2$.

Product of Negative Numbers

When two negative numbers are multiplied, their product is positive. This is a consistent rule in mathematics.

Here's why: consider that multiplying a number by $-1$ changes its sign. So, multiplying two negatives effectively reverses the sign twice, resulting in a positive. For instance, in our example of $-10$ and $-\frac{1}{5}$, after finding the product of their absolute values to be 2, we determine that:

$-10 \times -1 = 10$
$-1 \times -\frac{1}{5} = \frac{1}{5}$

These steps together give a positive result of 2.

Positive Results from Negative Multiplication

Multiplying two negative numbers always yields a positive result. This concept is often counterintuitive, but it is rooted in the rules of arithmetic.

For instance, think about repeatedly adding or subtracting negatives. When you multiply $-10$ by $-\frac{1}{5}$, you're essentially reversing directions twice, returning to a positive.

To recap, the steps are:

Identify the absolute values ($10$ and $\frac{1}{5}$).
Multiply these values to get 2.
Apply the rule that two negatives make a positive.

Therefore, $-10 \times -\frac{1}{5} = 2$.

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91影视

Find each product. $$ -10\left(-\frac{1}{5}\right) $$

Short Answer

Step by step solution

Understand the problem

Multiply the numbers

Determine the sign

Key Concepts

Absolute Values

Product of Negative Numbers

Positive Results from Negative Multiplication

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