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        

Porridge

KS 3 Short Challenge Level:

Challenge Level:1

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

Petrol Station

KS 3 Short Challenge Level:

Challenge Level:1

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

Almost Half Way

KS 3 Short Challenge Level:

Challenge Level:1

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

Tommy's Tankard

KS 3 Short Challenge Level:

Challenge Level:1

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?

Multiplication Magic Square

KS 3 Short Challenge Level:

Challenge Level:1

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

Magical Products

KS 3 Short Challenge Level:

Challenge Level:1

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?

Smashing Time

KS 3 Short Challenge Level:

Challenge Level:1

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

Talulah's Tulips

KS 3 Short Challenge Level:

Challenge Level:1

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?

Better Spelling

KS 3 Short Challenge Level:

Challenge Level:1

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.

Three Blind Mice

KS 3 Short Challenge Level:

Challenge Level:1

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?

Baby Boom

KS 3 Short Challenge Level:

Challenge Level:1

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

Valuable Percentages

KS 3 Short Challenge Level:

Challenge Level:1

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:

Challenge Level:1

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?

Bouncing Ball

KS 3 Short Challenge Level:

Challenge Level:1

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.

Bargain

KS 3 Short Challenge Level:

Challenge Level:1

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

Percentage Mad

KS 3 Short Challenge Level:

Challenge Level:1

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

The Grand Old Duke of York

KS 3 Short Challenge Level:

Challenge Level:1

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?

Half Way

KS 3 Short Challenge Level:

Challenge Level:1

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

Washing-up

KS 3 Short Challenge Level:

Challenge Level:1

What fraction of customers buy Kleenz after the advertising campaign?

Information Display

KS 3 Short Challenge Level:

Challenge Level:1

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?

Tennis Club

KS 3 Short Challenge Level:

Challenge Level:1

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?

Pride of Place

KS 3 Short Challenge Level:

Challenge Level:1

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

Second Half Score

KS 3 Short Challenge Level:

Challenge Level:1

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?

Meeting Point

KS 3 Short Challenge Level:

Challenge Level:1

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?

Jacob's Flock

KS 3 Short Challenge Level:

Challenge Level:1

How many sheep are in Jacob's flock?

Fractions of 1000

KS 3 Short Challenge Level:

Challenge Level:1

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

Mean Sequence

KS 3 Short Challenge Level:

Challenge Level:1

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

Share a Sheep

KS 3 Short Challenge Level:

Challenge Level:1

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

Ordering Fractions

KS 3 Short Challenge Level:

Challenge Level:1

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

Slightly Outnumbered

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Percentage of a Quarter

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Solitare

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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%?

Pied Piper

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Breakfast Time

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Peanut Harvest

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Tricky Fractions

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Too Close to Call

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Percentage Swap

KS 4 Short Challenge Level:

Challenge Level:1

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

Entrance Exam

KS 4 Short Challenge Level:

Challenge Level:1

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

A Drink of Water

KS 4 Short Challenge Level:

Challenge Level:1

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

Relative Angles

KS 4 Short Challenge Level:

Challenge Level:1

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

Antiques Roadshow

KS 4 Short Challenge Level:

Challenge Level:1

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

The Property Market

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Recurring Mean

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

2011 Digits

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Producing an Integer

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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?