Rational Numbers

You ask your class which fraction is larger [latex]\frac{9}{10}[/latex] or [latex]\frac{8}{9}[/latex]. Julian says it is [latex]\frac{9}{10}[/latex] because 9 is bigger than 8. Geoff says it is [latex]\frac{8}{9}[/latex] because 1/9 pieces are larger than 1/10 pieces. Is either of their logic correct? Can you help them to understand the answer without resorting to random “tricks” like cross-multiplying?

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