Fractions, Decimals, Percentages and Ratio - Short Problems


This is part of our collection of Short Problems.

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

Restful Sundays

KS 2 & 3 Short Challenge Level:

Challenge Level:1

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

Smashing Time

KS 2 & 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?

Slightly Outnumbered

KS 2 & 3 Short Challenge Level:

Challenge Level:1

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

Dividing by a Half

KS 2 & 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 46 - 2013
What is the value of 3 divided by one half?

Middle of the Fraction Road

KS 2 & 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 29 - 2012
Which fraction is halfway between one quarter and one eigth?

Better Spelling

KS 2 & 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.

Petrol Station

KS 2 & 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?

Valuable Percentages

KS 2 & 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?

Magical Products

KS 2 & 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?

Farthest Fraction

KS 2 & 3 Short Challenge Level:

Challenge Level:1

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

Shepherd's Flock

KS 2 & 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 26 - 2010
Does Joseph have too many sheep in his flock...

Question Setters

KS 3 Short Challenge Level:

Challenge Level:1

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?

Percentage Mad

KS 3 Short Challenge Level:

Challenge Level:1

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

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?

Televisual Technology

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 27 - 2012
Television screens have changed from the traditional 4:3 to widescreen 16:9. If a new television and an old television have the same area, what is the ratio of their widths?

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?

Tyre Wear

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 52 - 2008
A car with 5 tyres (four road tyres and a spare) travelled 30,000 km. All 5 tyres were used equally. How many kilometres' wear did each tyre receive?

Cover-up

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 49 - 2010
When I place a triangle over a small square, or cover a larger square with the same triangle, a certain proportion of each is covered. What is the area of the triangle?

Chocolate Multipliers

KS 3 Short Challenge Level:

Challenge Level:1

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

Inspector Remorse

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 49 - 2011
How long will it take Inspector Remorse to crack this crime spree?

Long Shadows

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 10 - 2012
If you know how long Meg's shadow is, can you work out how long the shadow is when she stands on her brother's shoulders?

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?

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?

A Leg to Stand On

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 30 - 2012
Can you work out the number of chairs at a cafe from the number of legs?

Off the Cuff

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 23 - 2012
Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?

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?

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?

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?

Family Fortune

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 8 - 2007
If three brothers will get £20 more if they do not share their money with their sister. How much money is there?

Too Close to Call

KS 3 Short Challenge Level:

Challenge Level:1

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

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?

Flapjack

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 37 - 2008
A recipe for flapjacks calls for a certain quantity of butter, sugar and oats. Given the amount of these ingredients I have, how many flapjacks can I make?

Marathon Mission

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 33 - 2012
Minnie trained more for the London Marathon this year, so her speed increased. By what percentage did her time decrease?

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?

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?

Fractions of Fractions

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 44 - 2013
If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

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?

Painting the Forth Bridge

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 14 - 2006
Given the rates at which men can paint, how long will it take them to paint the Forth Bridge?

Anulus Area

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 38 - 2011
Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

Percentage Swap

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Recurring Mean

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Spider Solitare

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Antiques Roadshow

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Fractions of 1000

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Cubic Fractions

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Ratio Riddle

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 8 - 2006
Can you work out the ratio $b:c$ given the ratios $a:b$ and $a:c$.

Producing an Integer

KS 3 & 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?

2011 Digits

KS 3 & 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?

Antifreeze

KS 3 & 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 4 - 2007
How much more antifreeze is needed to make the proportion 30%?

Flower Show

KS 3 & 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 7 - 2006
It takes four gardeners four hours to dig four circular flower beds, each of diameter 4 metres. How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?