Fractions

problem
Reductant ratios

Age

16 to 18

Challenge level

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

Age

11 to 14

Challenge level

Two fractions have been placed on a number line. Where should another fraction be placed?
problem
Fractions of 1000

Age

14 to 16

Challenge level

Find a simple way to compute this long fraction.
problem
Special sums and products

Age

11 to 14

Challenge level

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
problem
Do unto Caesar

Age

11 to 14

Challenge level

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?
$Unit fractions$

problem
Unit fractions

Age

11 to 14

Challenge level

Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
problem
Smaller and smaller

Age

7 to 14

Challenge level

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?
problem
Hello again

Age

11 to 14

Challenge level

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?
problem
Modular fractions

Age

16 to 18

Challenge level

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.
problem
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.