Fractions, Decimals and Percentages - Short Problems
Smashing Time
Weekly Problem 58 - 2012
Once granny has smashed some of her cups and saucers, how many cups are now without saucers?
Talulah's Tulips
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
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
Weekly Problem 23 - 2010
These numbers have been written as percentages. Can you work out which has the greatest value?
Bouncing Ball
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.
Percentage Mad
Weekly Problem 43 - 2013
What is 20% of 30% of 40% of £50?
Information Display
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?
Mean Sequence
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
Weekly Problem 46 - 2014
Which of these fractions has greatest value?
Tommy's Tankard
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
Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?
Magical Products
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
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?
Halfway
Can you find a number that is halfway between two fractions?
Pride of Place
Two fractions have been placed on a number line. Where should another fraction be placed?
Second Half Score
Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?
Between a Sixth and a Twelfth
The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.
Tricky Fractions
Use this series of fractions to find the value of x.
Too Close to Call
Weekly Problem 24 - 2012
Can you put these very close fractions into order?
Slightly Outnumbered
If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?
Peanut Harvest
A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?
A Drink of Water
Weekly Problem 43 - 2015
Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?
Entrance Exam
Dean finishes his exam strongly. Can you work out how many questions are on the paper if he gets an average of 80%?
Baby Boom
Which of the cities shown had the largest percentage increase in population?
Test Scores
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?
Tennis Club
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?
The Grand Old Duke of York
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?
Meeting Point
Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?
Porridge
To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?
Petrol Station
Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?
Recurring Mean
What is the mean of 1.2 recurring and 2.1 recurring?
Itchy's Fleas
Itchy the dog has a million fleas. How many fleas might his shampoo kill?
Bargain
Weekly Problem 11 - 2013
A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?
Percentage Unchanged
If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?
Washing-up
What fraction of customers buy Kleenz after the advertising campaign?
2011 Digits
Weekly Problem 10 - 2014
What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?
Solitare
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%?
Fractions of 1000
Find a simple way to compute this long fraction.
Breakfast Time
Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?
Antiques Roadshow
Last year, on the television programme Antiques Roadshow... work out the approximate profit.
Squeezed In
Weekly Problem 9 - 2017
What integer x makes x/9 lie between 71/7 and 113/11?
Producing an Integer
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?
Elephants and Geese
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?
The Property Market
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?