/*! 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 120 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 120

Perform the indicated operations. Begin by performing operations in parentheses. $$\left(\frac{1}{2}+\frac{1}{4}\right) \div\left(\frac{1}{2}+\frac{1}{3}\right)$$

Short Answer

Expert verified
The short answer is \( \frac{9}{10} \).

Step by step solution

01

Solve Numerator

Begin by solving the operation within parentheses in the numerator: \( \frac{1}{2} + \frac{1}{4} \). These are fractional numbers with different denominators. To add them, you need to find the least common multiple of 2 and 4, which is 4. Convert \(\frac{1}{2}\) to the equivalent fraction that has 4 as denominator by multiplying both the numerator and the denominator by 2. So, the equivalent fraction for \(\frac{1}{2}\) will be \(\frac{2}{4}\). Now both \(\frac{2}{4}\) and \(\frac{1}{4}\) have the same denominator and their addition would yield \(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).
02

Solve Denominator

Now solve the operation within parentheses in the denominator: \( \frac{1}{2} + \frac{1}{3}\). Here, the denominators are 2 and 3, so to add these fractions, you need to find the least common multiple of 2 and 3 which is 6. Convert both fractions to have the denominators as 6. So, \(\frac{3}{6}\) is the equivalent fraction for \( \frac{1}{2}\) and \(\frac{2}{6}\) is the equivalent one for \(\frac{1}{3}\). Thus, \(\frac{3}{6} + \frac{2}{6} = \frac{5}{6}\).
03

Peform Division

As per the problem statement, you need to perform the division \( \frac{3}{4} \div \frac{5}{6} \). In fractional division, change the division to multiplication and flip (find the reciprocal of) the second fraction. Then, the operation becomes \( \frac{3}{4} * \frac{6}{5} \). Multiply the numerators together for new numerator and denominators together for new denominator. \( \frac{3*6}{4*5} = \frac{18}{20} \). This can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \( \frac{18}{20} = \frac{9}{10}\).

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

Perform the indicated subtraction. $$4 \pi-(-12 \pi)$$

Perform the indicated subtraction. $$-2.06-(-2.06)$$

Perform the indicated subtraction. $$-\frac{4}{5}-\frac{1}{5}$$

Perform the indicated subtraction. $$\frac{2}{5}-\left(-\frac{1}{10}\right)$$

Simplify each series of additions and subtractions. $$-823-146-50-(-832)$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

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.