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laila [671]
3 years ago
6

Find the repeating decimal between -2 1/3 and -2 1/5.

Mathematics
1 answer:
Andrew [12]3 years ago
6 0

let's first off, make the mixed fractions to improper fractions and then <u>multiply one by the other's denominator</u>, that way both fractions have the same denominator, so let's start,

\bf \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}}~\hfill \stackrel{mixed}{2\frac{1}{5}}\implies \cfrac{2\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{11}{5}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{multiplying one by the other's denominator}}{\cfrac{7}{3}\cdot \cfrac{5}{5}\implies \boxed{\cfrac{35}{15}}\qquad \qquad \cfrac{11}{5}\cdot \cfrac{3}{3}\implies \boxed{\cfrac{33}{15}}} \\\\[-0.35em] ~\dotfill

\bf \boxed{-\cfrac{35}{15}}\rule[0.35em]{9em}{0.25pt}~~\underset{\underset{\textit{\large -2.66666666...}}{\uparrow} }{-\cfrac{34}{15}}~~\rule[0.35em]{9em}{0.25pt}\boxed{-\cfrac{33}{15}}

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