/*! 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 3 What is the value of \(\frac{\fr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 3

What is the value of \(\frac{\frac{2}{3}}{\frac{1}{6}} ?\)

Short Answer

Expert verified
The value is 4.

Step by step solution

01

Understand the Problem

The problem requires finding the value of the division of two fractions. Specifically, we need to find the value of \(\frac{\frac{2}{3}}{\frac{1}{6}}\).
02

Invert the Divisor

When dividing by a fraction, multiply by its reciprocal. The reciprocal of \(\frac{1}{6}\) is \(\frac{6}{1}\). So, the problem becomes multiplying \(\frac{2}{3}\) by \(\frac{6}{1}\).
03

Multiply the Fractions

To multiply fractions, multiply the numerators together and the denominators together. So, \(\frac{2}{3} \times \frac{6}{1} = \frac{2 \times 6}{3 \times 1} = \frac{12}{3}\).
04

Simplify the Result

Simplify the fraction \(\frac{12}{3}\). Divide the numerator and the denominator by their greatest common divisor, which is 3. So, \(\frac{12}{3} = 4\).

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 a Fraction
To understand fraction division, it's crucial to grasp the concept of the reciprocal. The reciprocal of a fraction simply means flipping it. For example, the reciprocal of \(\frac{1}{6}\) is \(\frac{6}{1}\). This is because a reciprocal essentially 'reverses' the fraction.
More formally, if you have a fraction \(\frac{a}{b}\), its reciprocal is \(\frac{b}{a}\).
This step is vital in fraction division problems because dividing by a fraction is the same as multiplying by its reciprocal.
Multiplying Fractions
Once you understand reciprocals, the next step is to multiply the fractions. To multiply fractions:
  • Multiply the numerators together.
  • Multiply the denominators together.
Using our problem, \(\frac{2}{3} \times \frac{6}{1}\):

  • Multiply the numerators: 2 \times 6 = 12.
  • Multiply the denominators: 3 \times 1 = 3.
This gives us \(\frac{12}{3}\).
Remember to always multiply straight across when dealing with fractions.
Simplifying Fractions
After multiplying, you often end up with a fraction that needs to be simplified. A simplified fraction is one where the numerator and the denominator have no common factors other than 1. To simplify \(\frac{12}{3}\), we need to divide both the numerator and the denominator by their greatest common divisor (GCD). This leads to our next concept.......
Greatest Common Divisor
The greatest common divisor (GCD) is the largest number that can divide both the numerator and the denominator without leaving a remainder. For the fraction \(\frac{12}{3}\), the GCD of 12 and 3 is 3.
So, divide both the numerator and the denominator by 3:
  • 12 \func{\div}{3} = 4
  • 3 \func{\div}{3} = 1
Therefore, \(\frac{12}{3} \rightarrow 4\). Simplifying the fraction confirms our final solution is 4.

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

What is the value of \(6(-3+1)-6(3-4) ?\)

How many positive factors of 54 are odd?

If \(x\) is an integer, how many values of \(x\) are there such that \(|x|<6\) and \(|x|<6 ?\)

What is the value of \((\sqrt{3}+3 \sqrt{27})(2 \sqrt{3}-\sqrt{27}) ?\)

When integer \(a\) is divided by \(5,\) the remainder is \(2 .\) When integer \(b\) is divided by \(5,\) the remainder is \(3 .\) What is the remainder when \(a \times b\) is divided by \(5 ?\)
See all solutions

Recommended explanations on English Textbooks

Essay Writing Skills

Read Explanation

Key Concepts in Language and Linguistics

Read Explanation

Lexis and Semantics Summary

Read Explanation

Essay Plan

Read Explanation

Semiotics

Read Explanation

Linguistic Terms

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.