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# Counting

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

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

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