Problem 59 Apply the appropriate property t... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 59

Apply the appropriate property to simplify the expression. $$-8(4-p)$$

Short Answer

Expert verified

The simplified expression is -16 + 8p

Step by step solution

- Identify the Property

The distributive Property is a(b + c) = ab + ac, and applies for any real a, b, c.

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Key Concepts

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

Simplifying Expressions

Simplifying expressions means making them easier to understand or work with. Usually, this involves combining like terms or using properties of operations.

In the given problem, we apply the Distributive Property to simplify $-8(4-p)$. First, we need to distribute \-8\ to both terms inside the parentheses.

Multiply \-8\ by 4: $-8 \times 4 = -32$
Multiply \-8\ by \-p\: $-8 \times -p = 8p$

This gives us $-32 + 8p$. So, $-8(4-p)$ simplifies to \-32 + 8p\. Notice that both multiplication operations were straightforward, following simple arithmetic rules.

It's important to take your time with each step to avoid mistakes!

Properties of Operations

Understanding the properties of operations helps you simplify algebraic expressions effectively. The main properties you will commonly use are:

Distributive Property: This tells us that $a(b + c) = ab + ac$. It's like handing out a to both b and c.
Commutative Property: This states that the order of addition or multiplication doesn't matter. For example, $a + b = b + a$.
Associative Property: This property explains that the way numbers are grouped in addition or multiplication doesn鈥檛 change their sum or product. For instance, $ (a + b) + c = a + (b + c)$.

In our problem, the Distributive Property is key. By distributing \-8\ across the terms inside the parentheses, we make the expression simpler and more manageable.

Practicing these properties will help you handle tougher algebraic problems in the future!

Prealgebra

Prealgebra sets the foundation for all algebra you'll learn later. It covers essential topics like:

Basic Arithmetic (addition, subtraction, multiplication, division)
Working with integers and rational numbers
Understanding factors and multiples
Recognizing and using the properties of operations

In this exercise, you鈥檙e required to use a key prealgebra skill: applying the Distributive Property to simplify an expression.

This step-by-step approach helps solidify your understanding and gives you the confidence to tackle more complex algebra problems. It鈥檚 essential to understand these core concepts deeply. Practice them regularly, and you'll find algebra becoming easier and even enjoyable!

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91影视

Apply the appropriate property to simplify the expression. $$-8(4-p)$$

Short Answer

Step by step solution

- Identify the Property

Key Concepts

Simplifying Expressions

Properties of Operations

Prealgebra

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