# Fractions, Decimals, Percentages and Ratio - November 2004, All Stages

## Problems

### Share Bears

##### Stage: 1 Challenge Level:

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

### Lots of Lollies

##### Stage: 1 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

### Fair Feast

##### Stage: 2 Challenge Level:

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

### Andy's Marbles

##### Stage: 2 Challenge Level:

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

### Orange Drink

##### Stage: 2 Challenge Level:

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

### The Tree and the Greenhouse

##### Stage: 2 Challenge Level:

Mum, Dad, Tim and Jill moved into a new house. If they cut down the big tree, will it miss the greenhouse?

### Water Lilies

##### Stage: 3 Challenge Level:

There are some water lilies in a lake. The area that they cover doubles in size every day. After 17 days the whole lake is covered. How long did it take them to cover half the lake?

### Peaches Today, Peaches Tomorrow....

##### Stage: 3 Challenge Level:

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?

### Ben's Game

##### Stage: 3 Challenge Level:

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

### Circuit Training

##### Stage: 4 Challenge Level:

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. . . .

### What a Joke

##### Stage: 4 Challenge Level:

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

### And So on - and on -and On

##### Stage: 5 Challenge Level:

Can you find the value of this function involving algebraic fractions for x=2000?

### Complex Partial Fractions

##### Stage: 5 Challenge Level:

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.

### FA Cup

##### Stage: 5 Challenge Level:

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!