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Chapter 1: Problem 133

Perform these computations. $$(-2)(0.35)$$

Short Answer

Expert verified
-0.70

Step by step solution

01

Understand the Task

Multiply the two given numbers: \[ (-2) \times 0.35 \]
02

Multiply the Absolute Values

First, multiply the absolute values of the numbers: \[ 2 \times 0.35 = 0.70 \]
03

Determine the Sign

Since we are multiplying a negative number by a positive number, the result will be negative: \[ (-2) \times 0.35 = -0.70 \]

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Key Concepts

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

multiplying negative and positive numbers
When multiplying numbers, it is essential to understand how the signs of the numbers affect the outcome. In multiplication, if one number is negative and the other is positive:
  • The product will always be negative.
  • This is because a negative and a positive number cancel each other out.
For instance, \[ (-2) \times 0.35 \] involves negative two and positive 0.35. The product, therefore, will be negative.
absolute values
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always positive. For example:
  • The absolute value of -2 is written as \| -2 \| = 2.
  • The absolute value of 0.35 is \| 0.35 \| = 0.35.
When multiplying, work with absolute values first, ignoring the signs initially, and then adjust the sign of the result. So, for the computation \[ (-2) \times 0.35 \], first multiply the absolute values: \[ 2 \times 0.35 = 0.70 \].
determining the sign of the product
Once you have multiplied the absolute values of the numbers, it is crucial to determine the correct sign for the product. Follow these rules:
  • If both numbers are positive, the product is positive.
  • If one number is positive and the other is negative, the product is negative.
  • If both numbers are negative, the product is positive.
For example, \[ (-2) \times 0.35 = -0.70 \] because one of the numbers is negative and the other is positive. Therefore, the final product is negative: \[ -0.70 \].

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