/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 98 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 98

In the following exercises, simplify using the distributive property. $$\frac{1}{2}(n+8)$$

Short Answer

Expert verified
\frac{1}{2}n + 4

Step by step solution

01

Identify the Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. In this case, the term outside the parenthesis is \(\frac{1}{2}\) and the terms inside the parenthesis are \(n\) and \(8\).
02

Multiply the First Term

Multiply \(\frac{1}{2}\) by \(n\): \(\frac{1}{2} \times n = \frac{1}{2}n\).
03

Multiply the Second Term

Next, multiply \(\frac{1}{2}\) by \(8\): \(\frac{1}{2} \times 8 = 4\).
04

Combine the Results

Add the results of your multiplications together: \(\frac{1}{2}n + 4\).

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.

Simplification
In algebra, simplification is an important skill. It makes expressions easier to work with. Simplification involves combining like terms and reducing expressions to their most basic form.
This is done to solve problems more easily.

For example, in our exercise, we started with an expression inside the parentheses, \((n + 8)\), and applied the distributive property to simplify it.
  • Simplification can involve different steps like combining like terms or reducing fractions.
  • It helps in reducing complex problems to more manageable ones.

      • By simplifying \(\frac{1}{2}(n + 8)\) into \(\frac{1}{2}n + 4\), we made the expression easier to handle in future calculations.
Multiplication
Multiplication in algebra involves scaling one number by another.
When applying multiplication to algebraic expressions, each part of the term in the parentheses is multiplied by the term outside the parentheses.

In our example, we needed to multiply \(\frac{1}{2}\) by each term inside the parentheses. First: \(\frac{1}{2} \times n = \frac{1}{2}n\)
  • This step ensures every term inside the parentheses is correctly scaled.
  • Using operations like \(\times\) is crucial in following rules of algebra accurately.
Next, we carefully multiplied \(\frac{1}{2}\) by \8\ to get 4.

By understanding these foundational steps, you can prevent mistakes and build complex solutions from simpler parts.
Algebraic Expressions
Algebraic expressions are a combination of variables, numbers, and operators like addition or multiplication. These are used to represent equations and formulas.
In our exercise, the expression inside the parentheses, \((n + 8)\), is an algebraic expression.

Knowing how to work with these expressions is key to succeeding in algebra.
  • Expressions involve variables which can change and constants which are fixed values.
  • You often simplify or solve for variables within these expressions.
Remember, practices like the distributive property help to manipulate these expressions into simpler or more useful forms.

Mastery of algebraic expressions will allow you to handle more complex problems and understand the language of algebra deeply.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

In the following exercises, simplity using the distributive property. $$ \frac{1}{3}(15 n-6) $$

In the following exercises, simplify using the commutative and associative properties. $$ 11 x+8 y+16 x+15 y $$

In the following exercises, convert between U.S. units. Round to the nearest tenth. A playground is 45 feet wide. Convert the width to yards.

In the following exercises, identify whether each example is using the identity of addition or multiplication. $$ -35(1)=-35 $$

In the following exercises, simplify the given expression. $$ \left(\frac{8}{15}+\frac{2}{9}\right)+\frac{7}{9} $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.