Answered: Complete the following inequalities…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Complete the following inequalities (<,=,>) and briefly explain how you knew which inequality sign to fill the
blank with. Use reasoning about fractions to answer these questions (do NOT use decimal values, common
denominators, and certainly not cross multiplying) , name your method in the blank and then explain that
reasoning below each comparison.
37/36 __ 42/41 ____________ 3/16 __ 7/32

Expert Solution

Step 1

$(1) First we have to compare \frac{37}{36} and \frac{42}{41} \frac{37}{36} = \frac{36 + 1}{36} = 1 + \frac{1}{36} \frac{42}{41} = \frac{41 + 1}{41} = 1 + \frac{1}{41} Now we know, \frac{1}{36} > \frac{1}{41} (Same numerator method .) Adding 1 both sides, we get 1 + \frac{1}{36} > 1 + \frac{1}{41} \frac{37}{36} > \frac{42}{41}$

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