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anyanavicka [17]

3 years ago

8

What are the next two terms after 1/8,2/7,3/6,4/5,...? And inductive reasoning for it

1 answer:

nydimaria [60]3 years ago

5 0

5/3 and 6/2 because the pattern shows that it adds one to the numerator while it deducts one from the denominator.

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Svet_ta [14]

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now, let's convert those mixed fractions to improper fractions and then subtract, bearing in mind our LCD will be 8.

$\bf \stackrel{mixed}{4\frac{5}{8}}\implies \cfrac{4\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{45}{8}-\cfrac{7}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)45~~-~~(4)7}{8}}\implies \cfrac{45-28}{8}\implies \cfrac{17}{8}\implies 2\frac{1}{8}$

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