Problem 64 $-2(8)=8(-2)$... [FREE SOLUTION]

91影视

Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 64

$-2(8)=8(-2)$

Short Answer

Expert verified

Therefore, the equation $-2(8)=8(-2)$ is indeed true, demonstrating the Commutative Law of Multiplication.

Step by step solution

Interpret the left hand side of the equation

The left hand side of the equation is $-2(8)$. According to order of operations, it's important to perform the multiplication first. Thus, multiplying -2 by 8 gives -16.

Interpret the right hand side of the equation

Next, evaluate the right hand side of the equation, $8(-2)$. Similarly, multiplying 8 by -2 also gives -16.

Comparison

Lastly, compare the two results. The left hand side $-2 * 8 = -16$ and the right hand side $8 * -2 = -16$. Hence, the equation $-2(8)=8(-2)$ is true because both sides are equal.

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Key Concepts

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

Order of Operations

The order of operations is crucial when solving mathematical expressions. It's a set of rules that tells us the sequence in which operations should be performed. This ensures everyone gets the same answer. Often remembered by the acronym PEMDAS:

P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction

For multiplication tasks like $-2(8)$, we focus on 'M' for multiplication. There's nothing preventing us from simply multiplying $-2$ and $8$.
Doing this step gives us $-16$, as outlined in step 1 of the original solution. By following the order of operations, equations are solved systematically and correctly.

Commutative Property

The commutative property of multiplication is a fundamental concept in mathematics. It tells us that numbers can be multiplied in any order, and the product will remain the same. This property makes calculations flexible and manageable.
In the exercise $-2(8) = 8(-2)$, both expressions yield $-16$. The process used:

Left side: Multiplying $-2$ by $8$
Right side: Multiplying $8$ by $-2$

Both steps produce the same product, perfectly illustrating the commutative property. This shows how multiplication does not depend on the order of numbers.

Negative Numbers Multiplication

Understanding multiplication with negative numbers is vital. When you multiply two numbers with differing signs, the result is always negative. Here's the logic:

Positive times Negative = Negative
Negative times Positive = Negative
Negative times Negative = Positive

In our exercise: $-2$ multiplied by $8$, and $8$ multiplied by $-2$ both produce $-16$. The differing signs ($-$ and $+$) between the numbers lead to this negative result, aligning with the rules of negative multiplication.
These basics make it easier to predict the sign of the product without actually computing it.

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91影视

\(-2(8)=8(-2)\)

Short Answer

Step by step solution

Interpret the left hand side of the equation

Interpret the right hand side of the equation

Comparison

Key Concepts

Order of Operations

Commutative Property

Negative Numbers Multiplication

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