Fractions, Decimals, Percentages and Ratio - Short Problems

A collection of short Stage 3 and 4 problems on fractions, decimals, percentages and ratio



Anulus Area

Stage: 3 and 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?

Producing an Integer

Stage: 3 and 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?

Inspector Remorse

Stage: 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

Stage: 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?

Off the Cuff

Stage: 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?

Too Close to Call

Stage: 3 Short Challenge Level: Challenge Level:1

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

Farthest Fraction

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Televisual Technology

Stage: 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?

Smashing Time

Stage: 2 and 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?

Middle of the Fraction Road

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

A Leg to Stand On

Stage: 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?

Baby Boom

Stage: 3 Short Challenge Level: Challenge Level:1

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

Marathon Mission

Stage: 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?

Percentage Mad

Stage: 3 Short Challenge Level: Challenge Level:1

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

Fractions of Fractions

Stage: 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?

Dividing by a Half

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Tennis Club

Stage: 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?

Flower Show

Stage: 3 and 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?

Ratio Riddle

Stage: 3 and 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 $a:c$.

Painting the Forth Bridge

Stage: 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?

Restful Sundays

Stage: 2 and 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?

Chocolate Multipliers

Stage: 3 Short Challenge Level: Challenge Level:1

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

Pied Piper

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Antifreeze

Stage: 3 and 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%?

Family Fortune

Stage: 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?

Porridge

Stage: 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?

Percentage Swap

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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

Recurring Mean

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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

Antiques Roadshow

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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

Information Display

Stage: 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?

Meeting Point

Stage: 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?

Flapjack

Stage: 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?

Question Setters

Stage: 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?

Tyre Wear

Stage: 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?

Slightly Outnumbered

Stage: 2 and 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?

Better Spelling

Stage: 2 and 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.

Valuable Percentages

Stage: 2 and 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?

Half Way

Stage: 3 Short Challenge Level: Challenge Level:1

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

Shepherd's Flock

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Pride of Place

Stage: 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?

Cover-up

Stage: 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?

Fractions of 1000

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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

Petrol Station

Stage: 2 and 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?

Magical Products

Stage: 2 and 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?

Three Blind Mice

Stage: 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?

Bargain

Stage: 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?

2011 Digits

Stage: 3 and 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?

Spider Solitare

Stage: 3 and 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%?

Cubic Fractions

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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