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Chapter 1: Problem 30

Perform each operation. SEE EXAMPLE 1. (OBJECTIVE 1) $$(-3)(11)$$

Short Answer

Expert verified
-33

Step by step solution

01

Identify the Numbers

First, identify the negative and positive numbers. In this instance, -3 is the negative number and 11 is the positive number.
02

Apply Multiplication

Next, apply the standard multiplication operation. Multiply 3 (the absolute value of -3) by 11. This results in 33.
03

Apply Sign Rule

Finally, apply the sign rule. The multiplication of a negative number and a positive number yields a negative result. Therefore, the final result is -33.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers that are less than zero. They are often used to represent values like debts or temperatures below freezing. Negative numbers have a minus sign (-) in front of them. For example, -3 means that we are talking about a value three less than zero.

In maths, negative numbers can be tricky for some students because they work differently from positive numbers. When dealing with operations like addition, subtraction, and especially multiplication, it鈥檚 important to remember their unique properties.
  • Negative numbers have a smaller value than zero.
  • They are found primarily on the left side of the number line.
  • When multiplied by another negative number, the result is positive.
Being comfortable with negative numbers is essential for performing operations effectively.
Exploring Positive Numbers
Positive numbers are numbers greater than zero. They are the numbers we count with in everyday life, like 1, 2, 3, etc. Seeing a positive number is simply a regular number, which often we don't write with a plus sign (+). For example, 11 is a positive number.

Understanding positive numbers is generally easier than negative numbers because they represent quantities or values that we can easily visualize or relate to in real life.
  • Positive numbers are always greater than zero.
  • They appear to the right of zero on the number line.
  • When multiplied by another positive, the result is positive.
Recognizing this allows us to perform basic operations with much more confidence.
Sign Rule in Multiplication
In multiplication, understanding how signs affect the result is crucial. The "sign rule" helps us determine the sign of the product when multiplying numbers:

  • A positive number multiplied by another positive number yields a positive result.
  • A negative number multiplied by a negative number also yields a positive result.
  • A positive number multiplied by a negative number, or vice versa (like -3 and 11), will result in a negative number.

In our original exercise, the multiplication of -3 (negative) and 11 (positive) resulted in -33. This is because the sign rule tells us that a negative times a positive equals a negative. Knowing this rule allows us to predict the sign of the result in any multiplication problem involving integers.

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