/*! 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 21 Perform the indicated operation.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 21

Perform the indicated operation. Write all results in lowest terms. $$-\frac{5}{6}+\frac{2}{5}$$

Short Answer

Expert verified
Answer: \(\frac{-13}{30}\)

Step by step solution

01

Find the Least Common Multiple of the denominators

Observe the denominators of both fractions, 6 and 5. Since they do not have any common factors, the least common multiple (LCM) of the denominators is equal to their product: \(6 \times 5 = 30\).
02

Rewrite the fractions with least common denominator

We must find an equivalent fraction for each of the given fractions that has the denominator of the LCM. We can multiply the numerator and denominator of each fraction by the necessary factor: $$ -\frac{5}{6} \cdot \frac{5}{5} = -\frac{25}{30} $$ $$ \frac{2}{5} \cdot \frac{6}{6} = \frac{12}{30} $$ So we can rewrite the given expression as \(-\frac{25}{30}+\frac{12}{30}\).
03

Perform the indicated operation

Now that both fractions have the same denominator, we can directly add them: $$ -\frac{25}{30}+\frac{12}{30} = \frac{-25 + 12}{30} = \frac{-13}{30} $$ The result is already in lowest terms, since the numerator and denominator do not share any common factors. So we have: $$ -\frac{5}{6}+\frac{2}{5} = \frac{-13}{30} $$

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!

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

Use the inequality symbols\(<\) or \(>\) to compare the following fractions. $$\frac{5}{12} \text { and } \frac{1}{3}$$
In Exercises \(32-37\), solve each equation for the unknown quantity. Check your answers. $$\frac{2}{3}+x=-\frac{1}{7}$$
In Exercises \(32-37\), solve each equation for the unknown quantity. Check your answers. $$\frac{5}{6}=\frac{1}{3}-x$$
Perform the indicated operation. Write all results in lowest terms. $$-\frac{3}{16}-\frac{3}{16}$$

Perform the indicated operation. Write all results in lowest terms. $$\frac{5}{8}-\frac{3}{8}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.