/*! 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 6 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 6

Perform the indicated operations and simplify. $$\frac{2}{13}+\frac{6}{13}$$

Short Answer

Expert verified
The simplified result is \( \frac{8}{13} \).

Step by step solution

01

Identify Similar Denominators

Both fractions in the expression have the same denominator, 13. This allows us to add them directly.
02

Add the Numerators

Since the denominators are the same, we only need to add the numerators. Add 2 and 6: \[ 2 + 6 = 8 \]
03

Write the Resulting Fraction

The added sum of the numerators forms the new numerator with the common denominator, 13. Thus, the resulting fraction is: \[ \frac{8}{13} \]
04

Simplify the Fraction

Determine if the fraction \( \frac{8}{13} \) can be simplified. Since 8 and 13 have no common factors other than 1, the fraction is already in its simplest form.

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 or subtracting fractions, it is essential to have a ***common denominator***. The denominator is the number below the fraction line, indicating into how many parts the whole is divided. In this exercise, both fractions have a denominator of 13, which is already common.

By having the same denominator, the fractions represent quantities split into the same number of parts, making the addition straightforward. You simply add the numerators, which are above the line, while maintaining the same denominator.

To sum up:
  • A common denominator allows for direct addition of numerators.
  • Both fractions here already have the common denominator of 13.
  • No need to adjust the fractions further before adding.
Simplifying Fractions
***Simplifying fractions*** involves reducing a fraction to its simplest form. This means the numerator and the denominator have no common factors apart from 1. It's an important step that helps make the fraction easier to understand and work with.

After performing an operation, like addition, always check if the resulting fraction can be simplified.

For our fraction, \( \frac{8}{13} \), observe these points:
  • 8 and 13 do not share any common factors except for 1.
  • The fraction is already in its simplest form, as we can't divide both parts by the same number greater than 1.
  • Simplification ensures clarity and accuracy in fraction operations.
Numerators and Denominators
Each fraction is made up of two parts: the ***numerator*** and ***denominator***.

The numerator is the number above the line, representing how many parts we are considering. In \( \frac{2}{13} \), the numerator is 2, and in \( \frac{6}{13} \), it is 6.

The denominator, on the other hand, is the number below the line, telling us into how many equal parts the whole is divided. Here, the denominator for both fractions is 13. This uniform denominator allows for the direct addition of numerators.

Remember these essentials:
  • Add numerators only after confirming common denominators.
  • The denominator in addition stays the same; it does not change.
  • Each part of the fraction has a distinct and important role.
Understanding the roles of numerators and denominators is key to mastering fraction addition.

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

Solve for the indicated variable. Each equation comes from the technical area indicated. \(S q+S p=S p q+p,\) for \(q \quad\) (computer design)

Perform the indicated operations. Each expression occurs in the indicated area of application. $$\frac{2 n^{2}-n-4}{2 n^{2}+2 n-4}+\frac{1}{n-1} \text { (optics) }$$

Solve the given equations and check the results. $$\frac{1}{x^{2}-x}-\frac{1}{x}+\frac{1}{1-x}=0$$

Set up appropriate equations and solve the given stated problems. All numbers are accurate to at least two significant digits. An engineer travels from Aberdeen, Scotland, to the Montrose oil field in the North Sea on a ship that averages \(28 \mathrm{km} / \mathrm{h}\). After spending \(6.0 \mathrm{h}\) at the field, the engineer returns to Aberdeen in a helicopter that averages \(140 \mathrm{km} / \mathrm{h}\). If the total trip takes \(15.0 \mathrm{h}\), how far is the Montrose oil field from Aberdeen?

Solve for the indicated variable. Each equation comes from the technical area indicated. \(R=k T_{2}^{4}-k T_{1}^{4},\) for \(k \quad\) (factor resulting denominator) (radiation)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

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.