This article extends and investigates the ideas in the problem "Stretching Fractions".
When if ever do you get the right answer if you add two fractions
by adding the numerators and adding the denominators?
Using an understanding that 1:2 and 2:3 were good ratios, start
with a length and keep reducing it to 2/3 of itself. Each time that
took the length under 1/2 they doubled it to get back within range.
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
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?
The Pythagoreans noticed that nice simple ratios of string length
made nice sounds together.
We only need 7 numbers for modulus (or clock) arithmetic mod 7
including working with fractions. Explore how to divide numbers and
write fractions in modulus arithemtic.
Relate these algebraic expressions to geometrical diagrams.
I need a figure for the fish population in a lake, how does it help to catch and mark 40 fish ?
Can you work out the parentage of the ancient hero Gilgamesh?
A personal investigation of Conway's Rational Tangles. What were
the interesting questions that needed to be asked, and where did
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .
A Sudoku with clues as ratios or fractions.
What fractions can you find between the square roots of 65 and 67?
The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.
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.
Imagine a strip with a mark somewhere along it. Fold it in the
middle so that the bottom reaches back to the top. Stetch it out to
match the original length. Now where's the mark?