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Chapter 10: Problem 6

Multiply. \(-20 \cdot 3\)

Short Answer

Expert verified
-60

Step by step solution

01

Identify the numbers involved

In the given exercise, the numbers involved are (-20) and 3.
02

Determine the multiplication sign rules

Recall the rule for multiplying numbers with different signs: a negative number times a positive number results in a negative product.
03

Multiply the absolute values

Multiply the absolute values of the two numbers: | (-20) | and | 3 |. This is simply 20 * 3.
04

Apply the sign

Using the rule from Step 2, since one number is negative (-20) and the other is positive (3), the product is negative. Therefore, the result is -60.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers that are less than zero. They are typically represented with a minus sign (-) in front of them. Some common characteristics of negative numbers include:
- They are the opposite of positive numbers.
- When represented on a number line, negative numbers are found to the left of zero.
- Combining a positive number and its negative counterpart will result in zero (e.g., 5 + (-5) = 0).
Understanding negative numbers is crucial when performing mathematical operations, such as multiplication or addition.
Absolute Values
The absolute value of a number is its distance from zero on the number line, regardless of direction. Absolute values are always non-negative. For example, the absolute value of -7 is 7, because -7 is 7 units away from zero. Similarly, the absolute value of 7 is also 7. In mathematical terms, the absolute value of a number x, denoted by |x|, is defined as:

\[ |x| = \begin{cases} x & \text{if } x \text{ is greater than or equal to 0} \ -x & \text{if } x \text{ is less than 0} \end{cases} \]When multiplying, we often use the absolute values of the numbers involved to simplify calculations, as demonstrated in our original exercise.
Sign Rules in Multiplication
Sign rules are essential when multiplying numbers. They help determine the sign of the resulting product. Here are the key sign rules you need to remember:

1. Positive 脳 Positive = Positive
2. Positive 脳 Negative = Negative
3. Negative 脳 Positive = Negative
4. Negative 脳 Negative = Positive

In the given exercise, we multiply -20 by 3. According to the rules:
- First, focus on the absolute values, 20 and 3.
- Next, multiply these absolute values: 20 * 3 = 60.
- Since we are multiplying a negative number (-20) by a positive number (3), the result will be negative: -60.
Understanding these sign rules can help you quickly solve multiplication problems involving negative numbers.

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