Problem 584 Multiply. $$ (-8.5)(1.69) ... [FREE SOLUTION]

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Chapter 1: Problem 584

Multiply. $$ (-8.5)(1.69) $$

Short Answer

Expert verified

-14.365

Step by step solution

Understand the Problem

We need to multiply two numbers: -8.5 and 1.69.

Multiply the Absolute Values

First, multiply the absolute values of the two numbers (ignore their signs).\[ 8.5 \times 1.69 \]

Perform the Multiplication

Calculate the product of 8.5 and 1.69.\[ 8.5 \times 1.69 = 14.365 \]

Apply the Sign

Since one of the numbers is negative and the other is positive, the product will be negative. Therefore, \[ -8.5 \times 1.69 = -14.365 \]

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Key Concepts

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

Absolute Value

Absolute value is a critical concept when multiplying numbers, especially if they are negative. The absolute value of a number is its distance from zero on the number line, without considering the direction (or sign). For example, the absolute value of both -3 and 3 is 3 because both numbers are 3 units away from zero.
When multiplying numbers, calculating the absolute value first can simplify the process. As shown in the problem, we first multiplied the absolute values of -8.5 and 1.69, resulting in 8.5 times 1.69. This step involves ignoring the negative sign initially and focusing purely on the magnitudes of the numbers.

Negative Numbers

Negative numbers represent values less than zero, often indicated with a minus sign (-). When multiplying with negative numbers, certain rules apply that affect the sign of the product.
One key rule is that when you multiply a negative number by a positive number, the result is always negative. This is why in our example, the product of -8.5 and 1.69 is -14.365.
Another rule is that multiplying two negative numbers results in a positive product. Understanding these rules can make it easier to work with negative numbers in multiplication.

Positive Numbers

Positive numbers are values greater than zero, and they are represented without any sign. Positive numbers are straightforward in multiplication since their signs do not change the product's sign when multiplied by another positive number.
However, when a positive number is multiplied by a negative one, the product takes the negative sign. This is why after calculating 8.5 times 1.69, we had to reapply the negative sign from -8.5, resulting in -14.365.
When multiplying, always consider the signs of the numbers involved to determine the product's final sign.

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91影视

Multiply. $$ (-8.5)(1.69) $$

Short Answer

Step by step solution

Understand the Problem

Multiply the Absolute Values

Perform the Multiplication

Apply the Sign

Key Concepts

Absolute Value

Negative Numbers

Positive Numbers

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