Induction Prove: Making Fractions 1/2 to 1

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In summary, induction prove is a mathematical method used to prove statements or equations that hold true for all natural numbers. In the case of making fractions 1/2 to 1, it can be used to show that the statement "all fractions between 1/2 and 1 can be made by adding 1/2 to itself" holds true for all natural numbers. The first step in using induction prove is to prove the statement holds true for the first natural number, and the next step is to assume it holds true for a certain natural number and use that assumption to prove it holds true for the next natural number. By using the principle of mathematical induction, this method allows us to prove a statement for an infinite set of numbers,
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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.
 
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This is a virtual duplicate of the thread found https://mathhelpboards.com/pre-calculus-21/fractions-can-you-make-proof-23555.html. Thread closed.
 

FAQ: Induction Prove: Making Fractions 1/2 to 1

What is induction prove and how does it apply to making fractions 1/2 to 1?

Induction prove is a mathematical method used to prove statements or equations that hold true for all natural numbers. In the case of making fractions 1/2 to 1, induction prove can be used to show that the statement "all fractions between 1/2 and 1 can be made by adding 1/2 to itself" holds true for all natural numbers.

What is the first step in using induction prove to make fractions 1/2 to 1?

The first step is to prove that the statement holds true for the first natural number, which is 1 in this case. This can be done by showing that 1/2 can be made by adding 1/2 to itself.

What is the next step in using induction prove to make fractions 1/2 to 1?

The next step is to assume that the statement holds true for a certain natural number, n. This is called the "inductive hypothesis." In this case, we assume that all fractions between 1/2 and 1 can be made by adding 1/2 to itself n times.

How do we use the inductive hypothesis to prove that the statement holds true for the next natural number?

Using the inductive hypothesis, we can show that the statement holds true for the next natural number, n+1. This is done by adding 1/2 to itself n+1 times, which is the same as adding 1/2 to itself n times and then adding 1/2 one more time. This proves that the statement holds true for n+1, and by the principle of mathematical induction, it holds true for all natural numbers.

What is the significance of using induction prove to make fractions 1/2 to 1?

Using induction prove allows us to prove a statement for an infinite set of numbers, in this case all natural numbers. This method is widely used in mathematics to prove statements and equations for all natural numbers, which would be impossible to do individually for each number.

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