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Chapter 2: Problem 87

Perform the indicated operation. $$18(-6)$$

Short Answer

Expert verified
The product is -108.

Step by step solution

01

Identify the Operation

The problem requires finding the product of 18 and -6. This means performing multiplication.
02

Apply the Multiplication Rule

Multiply the numbers as if both were positive: \( 18 \times 6 = 108 \).
03

Determine the Sign of the Product

Since one factor is positive (18) and the other is negative (-6), the product will be negative. Therefore, \( 18 \times -6 = -108 \).

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Key Concepts

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

integer multiplication
When you multiply integers, you're working with whole numbers which can be positive or negative. Multiplication of integers follows the same principles as multiplication of any numbers. It involves combining groups of numbers. For instance, when you multiply 18 by 6, you're essentially adding 18 six times.

Here鈥檚 a basic rundown:
- Take the two integers you need to multiply.
- Multiply them normally just as you would with positive numbers.
- Later, we will determine the sign.
negative numbers
Negative numbers are less than zero, represented with a minus sign (-). Unlike positive numbers, they signify a reduction, loss, or owing. When you multiply with negative numbers, the calculations follow a specific sign rule, detailed in the next section.

Remember:
- Treat the negative sign as a separate entity initially.
- Focus first on multiplying the absolute values (the positive values without the sign) of the numbers involved.
product sign rules
The product sign rules dictate the sign of the result when multiplying integers:
  • **Both numbers positive:** The product is positive. For example, 3 * 4 = 12.
  • **One number positive, one number negative:** The product is negative. For example, -3 * 4 = -12.
  • **Both numbers negative:** The product is positive because two negatives cancel out. For example, -3 * -4 = 12.

In the example given, 18(-6), you multiply 18 by 6 to get 108. Since one of the numbers is positive and the other is negative, the product鈥檚 sign will be negative, giving us -108.
basic arithmetic operations
In mathematics, the basic arithmetic operations are: addition, subtraction, multiplication, and division. Each operation has its own set of rules, but they often interplay, especially in more complex problems. Among these, multiplication is repeatedly combining the same numbers.

Understanding these operations with integers lays the groundwork for more advanced mathematics. Multiplication is particularly foundational because it reveals patterns and sets the stage for algebra and beyond. Practicing multiplication with different signs helps in understanding integer behavior better, ensuring a strong basic arithmetic foundation.

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Most popular questions from this chapter

One of the most famous blizzards in the United States was the blizzard of \(1888 .\) In one part of Nebraska, the temperature plunged from \(40^{\circ} \mathrm{F}\) to \(-25^{\circ} \mathrm{F}\) in \(5 \mathrm{hr}\). What was the average change in temperature during this time?

Fill in the blank with \(<,>,\) or \(=\) $$-44 \square-54$$

Translate each English phrase to a mathematical expression. Then simplify. 150 decreased by 75

Simplify. $$-1^{5}$$

Divide the real numbers, if possible. $$\frac{204}{-6}$$
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