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Chapter 1: Problem 2

Evaluate each of the following expressions, if possible. $$(+6)(-3)$$

Short Answer

Expert verified
The result is -18.

Step by step solution

01

Identify the operation

The given expression is \( (+6)(-3) \), which implies multiplication.
02

Multiply the numerical values

Multiply the absolute values of the numbers: \( 6 \times 3 = 18 \).
03

Determine the sign of the product

When multiplying a positive number \( +6 \) by a negative number \( -3 \), the result is negative. Thus, \( (+6)(-3) = -18 \).

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Key Concepts

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

Absolute Value
Absolute value signifies the distance of a number from zero on a number line without considering its direction. It is always a non-negative number. For example, the absolute value of both -3 and 3 is 3 because they are three units away from zero.

The absolute value of a number \(x\) is denoted by \(|x|\). In the given exercise, we first identify and use these absolute values to perform operations. So, for \(6\) and \(-3\), their absolute values are \(|6| = 6\) and \(|-3| = 3\).

Using absolute values helps simplify the multiplication process, which brings us to our next topic.
Multiplication of Integers
Multiplication of integers involves finding the product of two numbers. While multiplying, we often first consider the absolute values of the numbers, as shown in the step-by-step solution. If we have integers \(a\) and \(b\), represented by their absolute values \(|a|\) and \(|b|\), then we simply multiply these to get the numerical result.

For instance, to compute \((+6)(-3)\), we multiply the absolute values: \(|6| \times |3| = 18\). This approach makes the calculation straightforward and allows us to later address the sign of the product, relating it to the signs of the original integers.

Let's now delve deeper into the sign rules for multiplication.
Sign Rules for Multiplication
One of the core aspects of multiplying integers is understanding how their signs work. The rules are simple:

  • Positive \( \times \) Positive = Positive
  • Negative \( \times \) Negative = Positive
  • Positive \( \times \) Negative = Negative
  • Negative \( \times \) Positive = Negative

These rules help determine the sign of the final product after calculating the absolute values.

In the exercise, we multiply \(+\text{6}\) by \(-\text{3}\). According to our rules:
  • A positive (\(+6\)) \( \times \) a negative (\(-3\)) = Negative

Thus, the multiplication \((+6)(-3) = -18\).

Following these rules ensures that we handle the product's sign correctly, giving us the accurate final result.

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Most popular questions from this chapter

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$2 \frac{1}{3}$$

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$4.8$$

Evaluate the given expression. Remember to follow the order of operations. $$\frac{18-3(4-1)}{2 \cdot 3+3}$$

At the beginning of the month Carla's checking account had a balance of \(\$ 643.47,\) while at the end of the month the balance was \(-\$ 82.94 .\) If she made no deposits during this month, what was the total of the checks that Carla wrote during this month?

If possible, list three numbers that are members and three numbers that are not members of the given set. If it is not possible, explain why. \(\\{t | t \text { is a real number but not a rational number }\\}\)
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