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Word Problems/Comparing Fractions

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Question
Hello:

Is there a different method to compare fractions to determine which is larger than the other?

Here are two methods that I am aware of:

1. Convert the fractions to decimals and then compare the decimals.

2. Convert the denominators of the fractions to the same number then compare the denominators.

Is there a third possibility?

I thank you for your reply.

Answer
I don't know of any other way.

One thing to note: If the denominator has prime factors of 2 or 5, it converts to a number with a finite number of digits.  If there are other prime factors in the denominator, there will be an infinite number of digits in decimal format.

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