# Fractions, Decimals and Percentages - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Fractions, Decimals and Percentages.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Stage 3 ★★ Sheet 1 Solutions Sheet 2 Solutions Sheet 3 Solutions

### Three Blind Mice

##### KS 3 Short Challenge Level:

Weekly Problem 10 - 2013
Each of the three blind mice in turn ate a third of what remained of a piece of cheese. What fraction of the cheese did they eat in total?

### Talulah's Tulips

##### KS 3 Short Challenge Level:

Weekly Problem 10 - 2017
Talulah plants some tulip bulbs. When they flower, she notices something interesting about the colours. What fraction of the tulips are white?

### Restful Sundays

##### KS 3 Short Challenge Level:

Weekly Problem 17 - 2006
Granny says she is 84 years old, not counting her Sundays. How old is she?

### Valuable Percentages

##### KS 3 Short Challenge Level:

Weekly Problem 23 - 2010
These numbers have been written as percentages. Can you work out which has the greatest value?

### Test Scores

##### KS 3 Short Challenge Level:

Weekly Problem 10 - 2016
Ivan, Tibor and Alex sat a test and achieved 85%, 90% and 95% respectively. Tibor scored just one more mark than Ivan. How many marks did Alex get?

### Information Display

##### KS 3 Short Challenge Level:

Weekly Problem 7 - 2008
The information display on a train shows letters by illuminating dots in a rectangular array. What fraction of the dots in this array is illuminated?

### Bargain

##### KS 3 Short Challenge Level:

Weekly Problem 11 - 2013
A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?

### Chocolate Multipliers

##### KS 3 Short Challenge Level:

Weekly Problem 23 - 2006
Can you work out how many times more chocolate Peg has then Meg?

### Half Way

##### KS 3 Short Challenge Level:

Weekly Problem 24 - 2010
Can you find a number that is half way between these two fractions?

### Peter Piper

##### KS 3 Short Challenge Level:

Weekly Problem 21 - 2016
Peter Piper picked a peck of pickled peppers. How many more pecks must Peter Piper pick to fill a barrel?

### Almost Half Way

##### KS 3 Short Challenge Level:

Weekly Problem 26 - 2012
Which of these fractions is the largest?

### Bouncing Ball

##### KS 3 Short Challenge Level:

A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.

### Meeting Point

##### KS 3 Short Challenge Level:

Weekly Problem 32 - 2008
Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

### The Grand Old Duke of York

##### KS 3 Short Challenge Level:

Weekly Problem 44 - 2017
What percentage of his 10,000 men did the Grand Old Duke of York have left when he arrived back at the bottom of the hill?

### Pride of Place

##### KS 3 Short Challenge Level:

Weekly Problem 47 - 2010
Two fractions have been placed on a number line. Where should another fraction be placed?

### Washing-up

##### KS 3 Short Challenge Level:

What fraction of customers buy Kleenz after the advertising campaign?

### Smashing Time

##### KS 3 Short Challenge Level:

Weekly Problem 58 - 2012
Once granny has smashed some of her cups and saucers, how many cups are now without saucers?

### Question Setters

##### KS 3 Short Challenge Level:

Weekly Problem 44 - 2008
John, Peter, Rudolf, Susie and Tony decide to set some questions for the Schools Mathematical Challenge. Can you work out how long in total they spend setting questions?

### Porridge

##### KS 3 Short Challenge Level:

Weekly Problem 43 - 2006
To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?

### Fractions of 1000

##### KS 3 Short Challenge Level:

Weekly Problem 50 - 2010
Find a simple way to compute this long fraction.

### Second Half Score

##### KS 3 Short Challenge Level:

Weekly Problem 48 - 2016
Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?

### Baby Boom

##### KS 3 Short Challenge Level:

Weekly Problem 25 - 2012
Which of the cities shown had the largest percentage increase in population?

### Mean Sequence

##### KS 3 Short Challenge Level:

Weekly Problem 38 - 2009
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?

### Ordering Fractions

##### KS 3 Short Challenge Level:

Weekly Problem 46 - 2014
Which of these powers of fractions has greatest value?

### Jacob's Flock

##### KS 3 Short Challenge Level:

How many sheep are in Jacob's flock?

### Petrol Station

##### KS 3 Short Challenge Level:

Weekly Problem 15 - 2011
Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?

##### KS 3 Short Challenge Level:

Weekly Problem 43 - 2013
What is 20% of 30% of 40% of £50?

### Share a Sheep

##### KS 3 Short Challenge Level:

How can Jim share his sheep between his three children in the way he wants to?

### Multiplication Magic Square

##### KS 3 Short Challenge Level:

Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?

### Magical Products

##### KS 3 Short Challenge Level:

Weekly Problem 9 - 2013
Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

### Tommy's Tankard

##### KS 3 Short Challenge Level:

Weekly Problem 4 - 2017
Tommy's tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?

### Tennis Club

##### KS 3 Short Challenge Level:

Weekly Problem 6 - 2007
Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?

### Better Spelling

##### KS 3 Short Challenge Level:

Weekly Problem 12 - 2010
Can Emily increase her average test score to more than $80$%? Find out how many more tests she must take to do so.

### Pied Piper

##### KS 3 Short Challenge Level:

Weekly Problem 7 - 2007
How many rats did the Pied Piper catch?

### Solitare

##### KS 3 Short Challenge Level:

Weekly Problem 45 - 2014
After playing 500 games, my success rate at Solitare is 49%. How many games do I need to win to increase my success rate to 50%?

### Percentage of a Quarter

##### KS 3 Short Challenge Level:

Weekly Problem 50 - 2017
What percentage of a quarter is a fifth?

### Breakfast Time

##### KS 3 Short Challenge Level:

Weekly Problem 49 - 2016
Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?

### Slightly Outnumbered

##### KS 3 Short Challenge Level:

Weekly Problem 3 - 2010
If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?

### Too Close to Call

##### KS 3 Short Challenge Level:

Weekly Problem 24 - 2012
Can you put these very close fractions into order?

### Tricky Fractions

##### KS 3 Short Challenge Level:

Use this series of fractions to find the value of x.

### Peanut Harvest

##### KS 3 Short Challenge Level:

A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?

### Relative Angles

##### KS 4 Short Challenge Level:

Can you work out the angles of a triangle from the relationships between them?

### Percentage Swap

##### KS 4 Short Challenge Level:

Weekly Problem 47 - 2007
What is 50% of 2007 plus 2007% of 50?

### A Drink of Water

##### KS 4 Short Challenge Level:

Weekly Problem 43 - 2015
Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?

### Entrance Exam

##### KS 4 Short Challenge Level:

Dean finishes his exam strongly. Can you work out how many questions are on the paper if he gets an average of 80%?

##### KS 4 Short Challenge Level:

Weekly Problem 51 - 2007
Last year, on the television programme Antiques Roadshow... work out the approximate profit.

### 2011 Digits

##### KS 4 Short Challenge Level:

Weekly Problem 10 - 2014
What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

### Recurring Mean

##### KS 4 Short Challenge Level:

Weekly Problem 49 - 2007
What is the mean of 1.2 recurring and 2.1 recurring?

### The Property Market

##### KS 4 Short Challenge Level:

A property developer sells two houses, and makes a 20% loss on one and a 20% profit on the other. Overall, did he make a profit or a loss?

### Producing an Integer

##### KS 4 Short Challenge Level:

Weekly Problem 46 - 2011
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

### Squeezed In

##### KS 4 Short Challenge Level:

Weekly Problem 9 - 2017
What integer x makes x/9 lie between 71/7 and 113/11?

### Elephants and Geese

##### KS 4 Short Challenge Level:

Yesterday, at Ulaanbaatar market, a white elephant cost the same amount as 99 wild geese. How many wild geese cost the same amount as a white elephant today?