### There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

### Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

### Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

# Countdown Fractions

##### Stage: 3 and 4 Challenge Level:

This is a more challenging version of Countdown

Choose any 6 cards.

The top row always contains the numbers 1, 2, 3 and 4 and the bottom row contains a range of fractions, that changes according to the level of difficulty:
• Level 1: halves, quarters and eighths
• Level 2: halves, thirds, quarters, sixths and twelfths
• Level 3: halves, quarters, fifths, tenths and twentieths
• Level 4: halves, thirds, quarters, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths and sixtieths.

Select a level and click on "play" to set a target. The challenge is to hit the target with the numbers available using just addition and subtraction.

Each card can only be used once. It may not be necessary to use all the cards.

It is always possible to hit the target. Clicking on "Show a solution" will offer one possible way in which the target can be reached, but it will not necessarily be the most efficient solution.

You may like to take on the challenge on your own or choose to play it as a game in which the first to reach the target gets a point. First to 10 points wins.

An alternative game could set a time limit and require the players to get as close to the target as possible. Each player could start with 20 points and then points could be deducted according to how far from the target each player has reached - e.g.$\frac{1}{4}$ away from the target would mean that $\frac{1}{4}$ of a point was deducted. After a set number of rounds, the player with the highest score wins.

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