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Matching Fractions, Decimals and Percentages
Can you match pairs of fractions, decimals and percentages, and beat your previous scores?
Age 11 to 14 Short
Challenge Level
Answer: $\frac{111110}{111111} < \frac{333331}{333334} < \frac{222221}{222223}$
$$\frac{111110}{111111} = 1 - \frac{1}{111111} = 1 - \frac{6}{666666}$$ $$\frac{222221}{222223} = 1 - \frac{2}{222223} = 1 - \frac{6}{666669}$$ $$\frac{333331}{333334} = 1 - \frac{3}{333334} = 1 - \frac{6}{666668}$$ Now, $$\frac{6}{666669} < \frac{6}{666668} < \frac{6}{666666}$$ and so
$$\frac{111110}{111111} < \frac{333331}{333334} < \frac{222221}{222223}$$
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.