/*! 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 118 Explain how to do the division \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 118

Explain how to do the division \(\frac{a}{b} \div \frac{c}{d} \div \frac{e}{f}.\)

Short Answer

Expert verified
The simplified form of the division of these three fractions is \(\frac{a*d*f}{b*c*e}\).

Step by step solution

01

Rewrite the Divisions as Multiplications

Begin by changing the division operations into multiplication operations. Do this by taking each fraction that you're dividing by and flip it to find its reciprocal. So, \(\frac{a}{b} \div \frac{c}{d} \div \frac{e}{f}\) becomes \(\frac{a}{b} * \frac{d}{c} * \frac{f}{e}\).
02

Multiply the Fractions Numerator by Numerator and Denominator by Denominator

Multiply the fractions. Do this by multiplying the numerators (top number) to get a new numerator and multiplying the denominators (bottom number) to get a new denominator. The new fraction is \(\frac{a*d*f}{b*c*e}\).
03

Simplify the Fraction If You Can

Check if you can simplify the fraction. For this problem, we can't simplify the fraction \(\frac{a*d*f}{b*c*e}\) without knowing the variables' values. Therefore, the solution will remain as \(\frac{a*d*f}{b*c*e}\) unless given specific values for a, b, c, d, e, and f.

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
Understanding the concept of the reciprocal is essential in fraction division. Simply put, the reciprocal of a number or a fraction is what you multiply it by to get the number 1.
When dealing with fractions, taking the reciprocal involves swapping the numerator (the top number) and the denominator (the bottom number).
For example:
  • The reciprocal of \( \frac{a}{b} \) is \( \frac{b}{a} \).
  • If you have a whole number like 7, its reciprocal is \( \frac{1}{7} \).
The operation of division in fractions relies heavily on the notion of reciprocals.
When dividing by a fraction, we convert the division into a multiplication by using the reciprocal of the divisor, essentially changing the divisor into its flipped form and then proceeding as a multiplication problem.
Multiplying Fractions
Once you've got the hang of transforming division into multiplication using reciprocals, the next step is straightforward: multiply the fractions.
Unlike addition or subtraction, there's no common denominator required for multiplication.
The process involves two simple rules:
  • Multiply the numerators together to get the new numerator.
  • Multiply the denominators together to get the new denominator.
Following this method, the division problem \( \frac{a}{b} \div \frac{c}{d} \div \frac{e}{f} \) becomes \( \frac{a}{b} \times \frac{d}{c} \times \frac{f}{e} \), which then multiplies as \( \frac{a \times d \times f}{b \times c \times e} \).
This reduced problem is now simply a product of the numerators and the denominators.
Fraction Simplification
After finding the product of the fractions, the last but crucial step is simplifying the fraction where possible.
Simplification is the process of reducing a fraction to its smallest equivalent form.
To simplify a fraction:
  • Find the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by this GCD.
Consider the expression \( \frac{a \times d \times f}{b \times c \times e} \).
This fraction can only be simplified if there's a common factor between the top and bottom terms.
Without specific numbers, we sometimes cannot perform further simplifications, leaving the fraction in its multiplicative outcome.
Remember, having a simplified fraction helps in understanding and comparing sizes more intuitively.

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

Set up and solve a proportion. Out of a sample of 500 men's shirts, 17 were rejected because of crooked collars. How many crooked collars would you expect to find in a run of 15,000 shirts?

Set up and solve a proportion. An HO-scale model railroad engine is 9 inches long. If HO scale is 87 feet to 1 foot, how long is a real engine?

Write each expression in simplest form. If it is already in simplest form, so indicate. Assume that no denominators are \(0 .\) $$\frac{x^{2}-10 x+25}{25-x^{2}}$$

Write each expression in simplest form. If it is already in simplest form, so indicate. Assume that no denominators are 0. SEE EXAMPLE 9. (OBJECTIVE 3) $$\frac{x y+2 y+3 x+6}{x^{2}+5 x+6}$$

Set up and solve a proportion. A cologne can be made by mixing 3 drops of pure essence with 7 drops of distilled water. How many drops of water should be used with 42 drops of pure essence?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

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.