/*! 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 81 Reduce the given fraction to low... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 81

Reduce the given fraction to lowest terms. $$\frac{-12 y^{5}}{98 y^{6}}$$

Short Answer

Expert verified
\(\frac{-6}{49y}\)

Step by step solution

01

Identify the Common Factor

Start by identifying any common factors shared by the numerator and denominator. In this case, both the numerator (-12) and the denominator (98) are divisible by 2.
02

Divide by the Common Factor

Divide the numerator and the denominator by the greatest common factor, which is 2. This gives us:\[\frac{-12 \div 2}{98 \div 2} = \frac{-6}{49}\]
03

Simplify the Variables

The variable terms in the fraction are \(y^5\) in the numerator and \(y^6\) in the denominator. According to the laws of exponents, subtract the exponents when dividing like bases:\[\frac{y^5}{y^6} = y^{5-6} = y^{-1}\]This simplifies to \(\frac{1}{y}\).
04

Combine the Results

Combine the simplified numeric and variable terms to get the fully reduced fraction:\[\frac{-6}{49} \times \frac{1}{y} = \frac{-6}{49y}\]

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.

Understanding Common Factors
In mathematics, a common factor is a number that divides two or more numbers without leaving a remainder. When you're tasked with reducing a fraction to its lowest terms, finding the common factors is crucial. For example, in the given problem, both -12 and 98 have common factors. We first identify the smallest positive common factor, which is 2.
  • Identify numbers that equally divide both the numerator and the denominator.
  • In this case, 2 is the number that divides both -12 and 98 without leaving any remainder.
This commonality helps us in simplifying fractions effectively.
The Laws of Exponents
Exponents provide a shorthand way of writing repeated multiplication. The laws of exponents help simplify expressions involving the same base. In the problem, we encounter variable terms like \(y^5\) and \(y^6\).
  • When dividing two expressions with the same base, you subtract the exponents: \(a^m / a^n = a^{m-n}\).
  • For \(y^5 / y^6\), subtracting the exponents gives us \(y^{5-6}\) or \(y^{-1}\).
  • An exponent of -1 implies the reciprocal: \(y^{-1} = 1/y\).
Understanding these rules can greatly ease the process of simplifying algebraic fractions.
Simplifying Fractions
Simplifying fractions involves both numeric and variable components in the given expression. The process of reducing fractions combines the elimination of common factors and the application of exponent laws.
  • First, factor the numerator and denominator by their greatest common factor, observed earlier as 2.
  • Next, apply exponent laws to the variable parts to reduce \(y^5/y^6\) to \(1/y\).
  • Finally, recombine the simplified numeric and variable parts to acquire the fully reduced fraction, which yields \(\frac{-6}{49y}\).
By following these steps in sequence, you can reduce fractions to their simplest form efficiently.

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

The area of a triangle is 44 square inches. If the length of the base is \(5 \frac{1}{2}\) inches, find the height (altitude) of the triangle.

Multiply the fractions, and simplify your result. $$\frac{-3 y^{3}}{4} \cdot \frac{23}{12 y}$$

List the multiples the given numbers, then list the common multiples. Select the LCM from the list of common multiples. 10 and 6

Divide the fractions, and simplify your result. $$\frac{21}{8} \div 7$$

Add or subtract the fractions, as indicated, and simplify your result. $$\frac{1}{2}-\frac{1}{9}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

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.