Problem 800 Simplify using the distributive ... [FREE SOLUTION]

91影视

Chapter 1: Problem 800

Simplify using the distributive property. $$ -(5 p-4) $$

Short Answer

Expert verified

-5p + 4

Step by step solution

- Recognize the Expression

Identify the given expression: $- (5p - 4)$

- Apply the Distributive Property

Use the distributive property to multiply the negative sign with each term inside the parentheses. Multiply $-1$ by each term: $-1 \cdot 5p$ and $-1 \cdot -4$

- Simplify Each Term

Simplify the results of each multiplication: $-1 \cdot 5p = -5p$ and $-1 \cdot -4 = 4$

- Combine the Terms

Combine the simplified terms to get the final answer: $-5p + 4$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Simplifying Expressions

To solve algebraic problems effectively, it's essential to simplify expressions. Simplifying expressions means to make an algebraic expression as simple as possible. This involves reducing complex expressions into simpler forms.
This can include:

Combining like terms.
Applying algebraic properties, such as associative and commutative properties.
Using the distributive property.

In our given exercise, the expression $ - (5p - 4) $ seems complex. By recognizing that it can be simplified using the distributive property, we can make it easier to handle.

Algebraic Properties

Algebraic properties are the rules that govern the manipulation of expressions. These properties help in simplifying expressions and solving equations. Important properties include:

Distributive Property: It allows multiplication to be distributed over addition or subtraction, e.g., \ a(b + c) = ab + ac \.
Associative Property: This states that how numbers are grouped in addition/multiplication does not change their result, e.g., \ (a + b) + c = a + (b + c) \.
Commutative Property: This indicates that the order of numbers in addition/multiplication does not affect the result, e.g., \ a + b = b + a \.

In our solution, we use the distributive property to simplify the expression $ - (5p - 4) $. By distributing the negative sign, we multiply each term inside the parentheses by \ (-1) \.

Negative Multiplication

Negative multiplication involves multiplying numbers or variables that include negative signs. Remembering the basic rules can help a lot:

Multiplying two positive numbers gives a positive result, e.g., \ 2 \ times \ 3 = 6 \.
Multiplying a positive number by a negative number gives a negative result, e.g., \ -2 \ times \ 3 = -6 \.
Multiplying two negative numbers gives a positive result, e.g., \ -2 \ times \ -3 = 6 \.

For our exercise: \ - (5p - 4) \ becomes \ -1 \ times $ 5p $ and \ -1 \ times \ (-4) \. The first term results in \ -5p \ and the second in \ 4 \ after simplification. Combining these, we get \ -5p + 4 \.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify using the distributive property. $$ -(5 p-4) $$

Short Answer

Step by step solution

- Recognize the Expression

- Apply the Distributive Property

- Simplify Each Term

- Combine the Terms

Key Concepts

Simplifying Expressions

Algebraic Properties

Negative Multiplication

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.