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Determine the number of fractions in the pattern below that are expressed in lowest terms.

\(\frac{1}{2019},\frac{2}{2018},\frac{3}{2017},\dots\frac{1010}{1010}\)

 

Any explanation would be helpful!

 Jul 14, 2022
 #1
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Note that in every term, the numerator increases by 1, and the denominator decreases by 1. 

 

Because the first term starts in 1 and increases by 1, the number of terms is the last term. 

 

Can you take it from here?

 Jul 14, 2022
 #2
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Yeah, there are \(1010\) of them, but the question asks for the number of the fractions expressed in lowest terms.

Guest Jul 14, 2022
 #5
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Every other fraction has an even number on top and an even number on bottom, so those will reduce.  I don't know about the others.  

 Jul 14, 2022
 #6
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Note that in every term, the numerator increases by 1, and the denominator decreases by 1. 

 

Because the first term starts in 1 and increases by 1, the number of terms is the last term. 

 

Can you take it from here?

 Jul 14, 2022

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