Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Supposer and s are any two rational numbers. By definition of rational, r = and s= for some ---Select--- a b d Writer - s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r-s= Both the numerator and the denominator are integers because ---Select--- In addition, bd 0 by the ---Select--- Hence r - s is a ---Select--- of two integers with a nonzero denominator, and so by definition of rational, r- s is rational. ✓a, b, c, and d with ---Select---
Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Supposer and s are any two rational numbers. By definition of rational, r = and s= for some ---Select--- a b d Writer - s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r-s= Both the numerator and the denominator are integers because ---Select--- In addition, bd 0 by the ---Select--- Hence r - s is a ---Select--- of two integers with a nonzero denominator, and so by definition of rational, r- s is rational. ✓a, b, c, and d with ---Select---
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 84E
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Transcribed Image Text:Prove the following statement directly from the definition of rational number.
The difference of any two rational numbers is a rational number.
Proof: Supposer and s are any two rational numbers. By definition of rational, r = and s =
b
d
for some
r-s=
---Select---
Writers in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following.
a, b, c, and d with ---Select---
Both the numerator and the denominator are integers because --Select---
In addition, bd 0 by the ---Select---
Hence r s is a ---Select---✓of two integers with a nonzero denominator, and so by definition of rational, r- s is rational.
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