Induction Prove: Making Fractions 1/2 to 1

  • Context: MHB 
  • Thread starter Thread starter cshao123
  • Start date Start date
  • Tags Tags
    Induction
Click For Summary
SUMMARY

The discussion focuses on proving that all fractions between 1/2 and 1 can be generated starting from the fraction 1/1 using two specific rules. The first rule allows the transformation of a fraction a/b in lowest terms to b/2a. The second rule enables the combination of two fractions a/b and c/d in lowest terms to create a new fraction (a+c)/(b+d). This proof is a virtual duplicate of an earlier thread on Math Help Boards.

PREREQUISITES
  • Understanding of fractions and their lowest terms
  • Familiarity with mathematical induction principles
  • Basic knowledge of fraction operations (addition and multiplication)
  • Experience with proof techniques in mathematics
NEXT STEPS
  • Study mathematical induction proofs in detail
  • Explore the properties of fractions in lowest terms
  • Learn about the implications of fraction transformations
  • Investigate similar proofs in number theory
USEFUL FOR

Mathematics students, educators, and anyone interested in understanding the principles of fraction manipulation and mathematical proofs.

cshao123
Messages
5
Reaction score
0
Suppose you begin with the fraction 1/1. There are 2 rules: a)If you can make a fraction a/b where a/b is in its lowest terms, then you can also make b/2a. b)If you can make a/b and c/d where they are both in lowest terms, you can also make (a+c)/(b+d).

Prove that you can make all fractions between and including 1/2 and 1.
 
Mathematics news on Phys.org
This is a virtual duplicate of the thread found https://mathhelpboards.com/pre-calculus-21/fractions-can-you-make-proof-23555.html. Thread closed.
 

Similar threads

High School Understanding the relationship between ratios and fractions
  • · Replies 8 ·
Replies
8
Views
2K
MHB Which fractions can you make (with proof)?
  • · Replies 7 ·
Replies
7
Views
2K
High School How to prove this for every Arithmetic Progression?
  • · Replies 12 ·
Replies
12
Views
2K
MHB Prove $\frac{1}{3}\le \frac{u}{v} \le \frac{1}{2}$ with Triangle Sides
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Proving Goldbach's conjecture by induction (or why it doesn't seem to work)
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad What is meant by "convergent just preceding ##\frac{a}{b}##" ?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Solve Prove by Induction: 3^2n+1 + 2^n-1 Divisible by 7
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Are there any two pairs of integers with the same result in a specific function?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Questions regarding Kurepa's Conjecture
  • · Replies 1 ·
Replies
1
Views
2K
MHB Solve Odd Math Puzzle: a^2+b^2=k(ab+1)
  • · Replies 2 ·
Replies
2
Views
3K