/*! 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 65 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 65

In the following exercises, simplify. $$ \frac{8}{15}+\frac{5}{7}+\frac{2}{7} $$

Short Answer

Expert verified
\frac{23}{15}

Step by step solution

01

- Identify Common Denominators

When adding fractions, ensure that all fractions share a common denominator. Here, the denominators are 15, 7, and 7. Notice that two of the fractions, \(\frac{5}{7}\) and \(\frac{2}{7}\), already have a common denominator.
02

- Combine Fractions with the Same Denominator

Combine the fractions that have the same denominator: \(\frac{5}{7} + \frac{2}{7} = \frac{7}{7} = 1\). Now the expression is \(\frac{8}{15} + 1\).
03

- Convert Whole Number to Fraction

Convert the whole number 1 to a fraction with the same denominator as \(\frac{8}{15}\). That is, \(\frac{15}{15}\), so the expression is \(\frac{8}{15}+\frac{15}{15}\).
04

- Add Fractions with Common Denominator

Add the fractions using the common denominator: \(\frac{8}{15} + \frac{15}{15} = \frac{8+15}{15} = \frac{23}{15}\).

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, it's crucial to have the same bottom number, called the denominator. If fractions have different denominators, we cannot simply add them up. Instead, we need to convert each fraction so that all the denominators match. This is known as finding a common denominator. In our example, the denominators are 15, 7, and 7. Since \(\frac{5}{7}\) and \(\frac{2}{7}\) already share a common denominator (7), we can quickly combine them.
Simplifying Fractions
Simplifying fractions involves reducing them to their simplest form. This means rewriting the fraction so that the numerator (top number) and the denominator (bottom number) are as small as possible, but still equivalent in value. For example, adding the fractions \(\frac{5}{7}\) and \(\frac{2}{7}\) results in \(\frac{7}{7}\), which equals 1. Simplifying into whole numbers makes further arithmetic easier. Eventually, simplifying \(\frac{23}{15}\), if possible, will give us a more straightforward and cleaner result.
Converting Whole Numbers to Fractions
To add whole numbers to fractions, we can convert the whole number into a fraction with the same denominator as the fraction we're working with. This ensures all terms in our addition have a common denominator. In the exercise, after combining \(\frac{5}{7}\) and \(\frac{2}{7}\), we get 1. Converting 1 into a fraction with a denominator of 15 results in \(\frac{15}{15}\). Now, we can easily add this to \(\frac{8}{15}\), giving us \(\frac{8}{15} + \frac{15}{15} = \frac{23}{15}\).

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 using the commutative and associative properties. $$ \frac{14}{11} \cdot \frac{35}{9} \cdot \frac{14}{11} $$

In the following exercises, solve using the appropriate unversions. Use the formula\(F=\frac{9}{5} C+32\) to convert \(35^{\circ} \mathrm{C}\) to degrees \(\mathrm{F}\)

In the following exercises, find the additive inverse. $$ -32 $$

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

In the following exercises, simplify. $$ (n+6.75)+0.25 $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Geometry

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.