Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Fractions of 1000

Stage: 3 and 4 Short Challenge Level:
When multiplying the fractions together, the denominator of each fractio, apart from the last, cancels with the numerator of the next fraction.

We are left with the numerator 1 from the first fraction and the denominator 10 from the last, which gives $\frac{1}{10}$ of $1000$, i.e. $100$

This problem is taken from the UKMT Mathematical Challenges.
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