/*! 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 269 In the following exercises, find... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 269

In the following exercises, find each sum. $$\frac{-11 x}{5}+\frac{7 x}{5}$$

Short Answer

Expert verified
\[ \frac{-4x}{5} \]

Step by step solution

01

- Identify the common denominator

Notice that both fractions, \(\frac{-11x}{5}\) and \(\frac{7x}{5}\), have the same denominator, which is 5.
02

- Combine the numerators

Since the denominators are the same, combine the numerators \(-11x\) and \(7x\) while keeping the denominator the same. This gives us: \(\frac{-11x + 7x}{5}\).
03

- Simplify the numerator

Simplify \(-11x + 7x\) to get \(-4x\). Now the fraction is \(\frac{-4x}{5}\).

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.

common denominator
When adding fractions, the key is to have a **common denominator**. A common denominator is a shared bottom number of the fractions you want to add. In the exercise given, both fractions \(\frac{-11x}{5}\) and \(\frac{7x}{5}\) already have a common denominator of 5. This makes it easy to go to the next step since you don't need to adjust the denominators.
combining numerators
With a common denominator in place, the next step is **combining numerators**. The numerator is the top part of the fraction. Here, for \(\frac{-11x}{5}\) and \(\frac{7x}{5}\), you simply add the numerators together \-11x and 7x\ while keeping the denominator 5 the same. This combination gives: \(\frac{-11x + 7x}{5}\). This part of the process makes the fraction addition straightforward.
simplifying fractions
The last step is **simplifying fractions**. This means reducing the fraction to its simplest form. Simplifying can involve combining like terms, reducing the common factors, or just performing straightforward arithmetic operations. For the sum we have: \(-11x + 7x = -4x\), so our fraction becomes \(\frac{-4x}{5}\). Since \-4x\ and 5 don't have a common factor other than 1, we can't simplify further. Thus, \(\frac{-4x}{5}\) is the simplified form of your fraction.

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, simplify. $$\frac{\frac{5}{8}+\frac{1}{6}}{\frac{19}{24}}$$

Translate and solve. The sum of two-thirds and \(n\) is \(-\frac{3}{5}\)

In the following exercises, determine whether the each number is a solution of the given equation. $$ y+\frac{3}{5}=\frac{5}{9} $$ $$ (a)y=\frac{1}{2} $$ $$ (b)y=\frac{52}{45} $$ $$ (c)y=-\frac{2}{45} $$

In the following exercises, simplify. $$ -6 \frac{2}{5} \div 4 $$

In the following exercises, find the least common denominator. $$\frac{3}{4}, \frac{1}{6}, \text { and } \frac{5}{10}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied 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.