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Resources tagged with Calculating with fractions similar to Comparing Continued Fractions:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Calculating with fractions

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Comparing Continued Fractions

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these continued fractions is bigger and why?

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Not Continued Fractions

Stage: 4 and 5 Challenge Level: Challenge Level:1

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

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Fracmax

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.

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Fair Shares?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

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There's a Limit

Stage: 4 and 5 Challenge Level: Challenge Level:1

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

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And So on - and on -and On

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the value of this function involving algebraic fractions for x=2000?

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The Harmonic Triangle and Pascal's Triangle

Stage: 5

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.

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Archimedes and Numerical Roots

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

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Countdown Fractions

Stage: 3 and 4 Challenge Level: Challenge Level:1

Here is a chance to play a fractions version of the classic Countdown Game.

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Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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Ratios and Dilutions

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

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Investigating the Dilution Series

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which dilutions can you make using only 10ml pipettes?

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Reductant Ratios

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What does the empirical formula of this mixture of iron oxides tell you about its consituents?