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#### Resources tagged with Calculating with fractions similar to Golden Fractions:

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### There are 18 results

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

### Not Continued Fractions

##### Age 14 to 18 Challenge Level:

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

### Comparing Continued Fractions

##### Age 16 to 18 Challenge Level:

Which of these continued fractions is bigger and why?

### The Harmonic Triangle and Pascal's Triangle

##### Age 16 to 18

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

### There's a Limit

##### Age 14 to 18 Challenge Level:

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?

### More Twisting and Turning

##### Age 11 to 16 Challenge Level:

It would be nice to have a strategy for disentangling any tangled ropes...

### All Tangled Up

##### Age 14 to 18 Challenge Level:

Can you tangle yourself up and reach any fraction?

### A Swiss Sum

##### Age 16 to 18 Challenge Level:

Can you use the given image to say something about the sum of an infinite series?

### Fair Shares?

##### Age 14 to 16 Challenge Level:

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?

### Fracmax

##### Age 14 to 16 Challenge Level:

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.

### Lower Bound

##### Age 14 to 16 Challenge Level:

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

### Harmonic Triangle

##### Age 14 to 16 Challenge Level:

Can you see how to build a harmonic triangle? Can you work out the next two rows?

### Countdown Fractions

##### Age 11 to 16 Challenge Level:

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

### Archimedes and Numerical Roots

##### Age 14 to 16 Challenge Level:

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?

##### Age 11 to 16 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

### And So on - and on -and On

##### Age 16 to 18 Challenge Level:

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

### Investigating the Dilution Series

##### Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

### Reductant Ratios

##### Age 16 to 18 Challenge Level:

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

### Ratios and Dilutions

##### Age 14 to 16 Challenge Level:

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