/*! 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 86 Perform the indicated operation.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 86

Perform the indicated operation. $$-\frac{5}{12} \div \frac{15}{32}$$

Short Answer

Expert verified
The result of the operation is \(-\frac{8}{9}\)

Step by step solution

01

Calculate the reciprocal of the second fraction

The given second fraction is \(\frac{15}{32}\). The reciprocal of this fraction is found by interchanging the numerator and the denominator. So, the reciprocal of \(\frac{15}{32}\) is \(\frac{32}{15}\).
02

Change the division operation to multiplication

A division of fractions can be converted to multiplication by multiplying the first fraction with the reciprocal of the second fraction. Hence the expression changes to: \(-\frac{5}{12} \times \frac{32}{15}\).
03

Multiply the fractions

To multiply the fractions, multiply the numerators together and the denominators together. Thus, the multiplication becomes \(\frac{-5 \times 32}{12 \times 15}\) which simplifies to \(-\frac{160}{180}\).
04

Simplify the fraction

The fraction \(-\frac{160}{180}\) can be simplified to \(-\frac{8}{9}\) by dividing the numerator and denominator by their highest common factor, which is 20.

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.

Reciprocal of Fractions
In mathematics, the reciprocal of a fraction is what you get when you flip the fraction upside down.Think of it like reversing the roles of the numerator and the denominator.
For example, if you have the fraction \(\frac{15}{32}\), its reciprocal will be \(\frac{32}{15}\). This transformation is essential when dividing fractions.
  • Why do we find the reciprocal? When dividing by a fraction, you multiply by its reciprocal. This is a fundamental rule of fraction division.
  • How to find it? Simply swap the numerator and the denominator.
Understanding this process makes the operation of dividing fractions much simpler and more straightforward.
Multiplying Fractions
Once you have converted division into multiplication using the reciprocal, the next step is to multiply the fractions. Fraction multiplication is straightforward: you just multiply the numerators to get the new numerator, and the denominators to get the new denominator.
So in our example, change \(-\frac{5}{12} \div \frac{15}{32}\) to \(-\frac{5}{12} \times \frac{32}{15}\). Then, multiply the numbers:
  • Numerator: \(-5 \times 32 = -160\)
  • Denominator: \(12 \times 15 = 180\)
This results in \(-\frac{160}{180}\). Just ensure you align multiplication of corresponding numerators and denominators to avoid errors.
Simplifying Fractions
After multiplication, the final step is simplifying the result to its lowest terms.Simplifying a fraction involves finding the greatest common factor (GCF) of the numerator and the denominator and dividing them by this number.For \(-\frac{160}{180}\), the GCF is 20.
  • Divide the Numerator: \(-160 \div 20 = -8\)
  • Divide the Denominator: \(180 \div 20 = 9\)
Finally, we get \(-\frac{8}{9}\), which cannot be simplified further. A properly simplified fraction is easier to interpret and ensures the result is as precise and neat as possible.

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

Subtract. $$-9-4$$

Subtract. $$-4-(-4)$$

Given that \(x\) is an integer, find all values of \(x\) for which \(|x|<5\)

Find the temperature after a rise of \(9^{\circ} \mathrm{C}\) from \(-6^{\circ} \mathrm{C}\)

The boiling point of oxygen is \(-182.962^{\circ} \mathrm{C}\). Oxygen's melting point is \(-218.4^{\circ} \mathrm{C} .\) What is the difference between the boiling point and the melting point of oxygen?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.