mathematics:

# Fractions over 7

For fractions over 7, remember 142857, since 1∕7=0.142857... Not difficult, since you multiply 7 by 2 to get 14, again by 2 to get 28 and finally by 2 to get 56 but since it's the last, we round it to 57 (just mnemo-logic). How do you cycle this number from least to greatest? 142857, 285714, 428571, 571428, 714285 and 857142. These give you the decimals for 2∕7, 3∕7, 4∕7, 5∕7 and 6∕7.

https://www.geogebra.org/m/bphzn6eh


# Triple proportions

Three workers paint 4 m² in 2 h. How long will it take for 6 workers to paint 100 m²? How to write \"hours per worker per m²? h⋅w∕m²? h∕(w⋅m²)? Fix one quantity, for example the area to be painted. Then, h and w must be such that either h⋅w or h∕w is constant. If there are more workers, less time will be needed, so h⋅w is constant. Now leave w constant. Then, more area to be painted needs more time, so h∕m² is constant. This means that the ratio is written as h⋅w∕m², so that 2⋅3∕4 = 3∕2 is our ratio. Then, 6 workers to paint 100 m² will take x hours. This means 3/2 = 6⋅x∕100, which implies x = 25 h.