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Chapter 2: Problem 79

In Exercises 79-84, evaluate the expression. \((-6)(-13)\)

Short Answer

Expert verified
The product of \((-6)(-13)\) is 78.

Step by step solution

01

Understand the Rule

In integers, the product of two negative numbers is a positive number. It's based on the rule that a negative times a negative gives a positive.
02

Perform the Operation

Evaluate \((-6)(-13)\) by multiplying 6 and 13 to get 78.
03

Apply the Rule

Since it was earlier concluded that the product of two negative numbers is positive, the product of \((-6)(-13)\) is a positive 78.

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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 essential in mathematics. They represent values that are less than zero. These numbers are commonly used when talking about debts or temperatures below freezing.
You can identify negative numbers by the minus sign (-) in front of them. They are opposite of positive numbers.

For example:
  • -2 is a negative number, meaning 2 less than zero.
  • -10 represents a drop in elevation.
When multiplying negative numbers, it's crucial to remember this key rule: multiplying two negative numbers results in a positive number.
Here's why:
  • Think of the first negative number as an instruction to "reverse, or do the opposite of" the second number.
  • Then, the second negative number also tells us to "reverse" again, leaving us with the original positive direction.
This is why the product of two negative numbers is positive.
Properties of Operations
Properties of operations help simplify and solve mathematical problems. They are rules that describe how numbers interact.
Two important properties are:
  • Commutative Property: This property tells us that the order of numbers can be switched without changing the result. For example, when multiplying, \(a \times b = b \times a\).
  • Associative Property: This property allows us to group numbers differently. In multiplication, it means \(a \times (b \times c) = (a \times b) \times c\).
Understanding these properties is helpful in simplifying complex calculations and clarifying the way mathematical operations can be performed. These properties apply to both positive and negative numbers.
Knowing them can greatly streamline solving problems involving multiplication or addition.
Evaluation of Expressions
Evaluating expressions means finding their value. It involves substituting numbers for variables and carrying out operations as indicated.
When evaluating expressions, ensure you follow the proper order of operations:
  • Parentheses: Solve expressions inside parentheses first.
  • Exponents: Evaluate any powers or roots next.
  • Multiplication and Division: These operations come third, carried out from left to right.
  • Addition and Subtraction: Finally, perform these operations from left to right.
Remembering the acronym PEMDAS can help recall this order.
In the exercise \((-6) \times (-13)\), apply the rule for multiplying negative numbers.
Calculate the absolute values first: \(6 \times 13 = 78\).
Then apply the rule: since two negatives equal a positive, the result is \(+78\).
By evaluating expressions properly, you ensure accuracy and correctness in your calculations.

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