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Chapter 2: Problem 100

Evaluate the expression. $$-16+(-6) \cdot(-8)$$

Short Answer

Expert verified
32

Step by step solution

01

Solve the Multiplication

Begin by solving the multiplication within the expression. That is \(-6 \cdot -8\), which equals 48. Rule in mathematics: the product of two negative numbers is a positive number.
02

Perform the Addition

Now, replace in the original equation the multiplication expression with the result obtained at step 1. The expression is now \(-16 + 48\). This equals 32.
03

Solution

The result of the expression \(-16+(-6) \cdot(-8)\) after following the order of operations is 32. Always remember to follow the order of operations and that the product of two negative numbers is a positive number.

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Key Concepts

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

Expression Evaluation
When faced with an algebraic expression like \(-16 + (-6) \cdot (-8)\), the task is to evaluate or simplify it down to a single number.The goal is to follow a given set of mathematical rules known as the Order of Operations.This order dictates which mathematical operations should be performed first to ensure accurate and consistent results.

This can be remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).This expression contains multiplication and addition, so according to the order:
  • The multiplication \((-6) \cdot (-8)\) must be completed first.
  • Once the first operation is resolved, move to the addition by plugging the result into the expression.
Always tackle operations one step at a time to avoid mistakes.
Multiplication of Integers
Multiplying integers, especially when dealing with negative numbers, is made simple by understanding the basic rules.These apply regardless of whether you're multiplying just two numbers or more.

For \((-6) \cdot (-8)\), both numbers are negative. The rule to remember is:
  • When multiplying two integers with the same sign, the result is positive.
  • Negative \(\times\) Negative = Positive
  • So, \((-6) \cdot (-8) = 48\)
By mastering these rules, you can tackle more complex expressions effortlessly.
Addition with Integers
After resolving the multiplication, you're left with a new expression: \(-16 + 48\). Now, focus on adding integers. This involves a few intuitive steps:
  • If both numbers were positive or negative, you'd simply add their absolute values and keep the original sign.
  • In this case, \(-16\) is negative and 48 is positive.
The approach here is to subtract the smaller absolute value from the larger one:
  • Subtract 16 (absolute value of \(-16\)) from 48.
  • This gives 32, and since 48 is positive, the result remains positive.
This intuitive balance helps manage expressions with mixed signs effectively.

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Most popular questions from this chapter

BUYING JEANS You have 58 dollar, and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a \(6 \%\) sales tax. If \(x\) represents the cost of the jeans, then the following inequality is a model that shows how much you can spend on the jeans. $$ x+20+0.06(x+20) \leq 58 $$ If the jeans cost \(\$ 35,\) can you buy both the T-shirt and the jeans?

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ -r(r-9) $$

Evaluate the expression. $$ 17+100 \div 25-5 $$

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ -x^{3}+2 x\left(x-x^{2}\right) $$

Evaluate the expression. $$ 89-8 \cdot 5-27 $$
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