/*! 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 237 Explain how you find the recipro... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 237

Explain how you find the reciprocal of a fraction

Short Answer

Expert verified
Swap the numerator and denominator.

Step by step solution

01

- Identify the Numerator and Denominator

A fraction is composed of two parts: a numerator (the top number) and a denominator (the bottom number). For example, in the fraction \(\frac{a}{b}\), \(a\) is the numerator and \(b\) is the denominator.
02

- Swap the Numerator and Denominator

To find the reciprocal of a fraction, simply exchange the positions of the numerator and the denominator. Therefore, the reciprocal of \(\frac{a}{b}\) is \(\frac{b}{a}\).
03

- Simplify If Necessary

If the resulting fraction can be simplified further, divide the numerator and the denominator by their greatest common divisor (GCD) to get the simplified reciprocal.

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.

Numerator and Denominator
When working with fractions, it's important to understand the roles of the numerator and denominator. In a fraction like \(\frac{a}{b}\), the numerator is the top number and represents how many parts of the whole we have. The denominator is the bottom number and it shows into how many equal parts the whole is divided.

For example, in the fraction \(\frac{3}{4}\), 3 is the numerator, and 4 is the denominator. This tells us that the whole is divided into 4 equal parts, and we have 3 of those parts.

Understanding numerators and denominators is crucial because it helps you manipulate and understand fractions better when performing operations such as finding reciprocals.
Simplify Fractions
Simplifying fractions means making the fraction as simple as possible. We do this by dividing the numerator and the denominator by their greatest common divisor (GCD).

For example, let's simplify the fraction \(\frac{8}{12}\):
  • First, identify the GCD of 8 and 12. The GCD of 8 and 12 is 4.
  • Next, divide both the numerator and the denominator by their GCD: \(\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}\).

This simplified form, \(\frac{2}{3}\), is equivalent to \(\frac{8}{12}\). Simplifying fractions often makes them easier to work with and understand.

You'll use this concept when finding the reciprocal of a fraction. After swapping the numerator and denominator, you should always check if you can simplify the new fraction.
Greatest Common Divisor
The greatest common divisor (GCD) of two numbers is the largest number that can divide both of them without leaving a remainder.

To find the GCD:
  • List the factors of both numbers. For example, for numbers 18 and 24:
    Factors of 18: 1, 2, 3, 6, 9, 18
    Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  • Identify the greatest common factor in both lists. In this case, it鈥檚 6.

So, the GCD of 18 and 24 is 6.

Using the GCD helps simplify fractions, which is a key step when working with reciprocals. If your result after swapping the numerator and denominator is \(\frac{18}{24}\), you can use the GCD to simplify it to \(\frac{3}{4}\), making your answer clearer and easier to understand.

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

In the following exercises, simplify. $$ 19 a+44-19 a $$

In the following exercises, simplify. $$ 12\left(\frac{5}{6} p\right) $$

In the following exercises, simplify using the Distributive Property. $$ 18-4(x+2) $$

In the following exercises, simplify using the Distributive Property. $$ -(3 x-7) $$

In your own words, state the Associative Property of addition.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

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.