Fractions

problem

Fractions Made Faster

Age

7 to 11

Challenge level

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!
problem

Pythagoras' Comma

Age

14 to 16

Challenge level

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.
problem

Percentage Swap

Age

14 to 16

Challenge level

What is 50% of 2007 plus 2007% of 50?
problem

Recurring Mean

Age

14 to 16

Challenge level

What is the mean of 1.2 recurring and 2.1 recurring?
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.
$Unit fractions$

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?