List

Fractions, Decimals and Percentages - Short Problems

Ordering Fractions
problem

Ordering fractions

Age
11 to 14
Challenge level
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Weekly Problem 46 - 2014
Which of these fractions has greatest value?
Multiplication Magic Square
problem

Multiplication magic square

Age
11 to 14
Challenge level
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Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?
Farthest fraction
problem

Farthest fraction

Age
11 to 14
Challenge level
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Which of these fractions is the largest?
Tommy's Tankard
problem

Tommy's tankard

Age
11 to 14
Challenge level
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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?
Talulah's Tulips
problem

Talulah's tulips

Age
11 to 14
Challenge level
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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?
Smashing Time
problem

Smashing time

Age
11 to 14
Challenge level
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Weekly Problem 58 - 2012
Once granny has smashed some of her cups and saucers, how many cups are now without saucers?
Percentage Mad
problem

Percentage mad

Age
11 to 14
Challenge level
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Weekly Problem 43 - 2013
What is 20% of 30% of 40% of £50?
Jacob's Flock
problem

Jacob's flock

Age
11 to 14
Challenge level
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How many sheep are in Jacob's flock?
Bouncing ball
problem

Bouncing ball

Age
11 to 14
Challenge level
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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.
Information Display
problem

Information display

Age
11 to 14
Challenge level
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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
problem

Mean sequence

Age
11 to 14
Challenge level
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Weekly Problem 38 - 2009
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?
Better Spelling
problem

Better spelling

Age
11 to 14
Challenge level
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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
problem

Valuable percentages

Age
11 to 14
Challenge level
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Weekly Problem 23 - 2010
These numbers have been written as percentages. Can you work out which has the greatest value?
Second Half Score
problem

Second half score

Age
11 to 14
Challenge level
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Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?
Placeholder: several colourful numbers
problem

Smallest fraction

Age
11 to 14
Challenge level
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Which of these is the smallest?
Placeholder: several colourful numbers
problem

Charlie's money

Age
11 to 14
Challenge level
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How much money did Charlie have to begin with?
Halfway
problem

Halfway

Age
11 to 14
Challenge level
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Can you find a number that is halfway between two fractions?
Pride of Place
problem

Pride of place

Age
11 to 14
Challenge level
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Two fractions have been placed on a number line. Where should another fraction be placed?
Placeholder: several colourful numbers
problem

Between a sixth and a twelfth

Age
11 to 14
Challenge level
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The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.
Magical Products
problem

Magical products

Age
11 to 14
Challenge level
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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
problem

Three blind mice

Age
11 to 14
Challenge level
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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?
Too Close to Call
problem

Too close to call

Age
11 to 14
Challenge level
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Weekly Problem 24 - 2012
Can you put these very close fractions into order?
Peanut Harvest
problem

Peanut harvest

Age
11 to 14
Challenge level
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A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?
tricky fractions
problem

Tricky fractions

Age
11 to 14
Challenge level
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Use this series of fractions to find the value of x.
Slightly Outnumbered
problem

Slightly outnumbered

Age
11 to 14
Challenge level
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If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?
Placeholder: several colourful numbers
problem

How shady?

Age
11 to 14
Challenge level
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What fraction of this triangle is shaded?
A Drink of Water
problem

A drink of water

Age
14 to 16
Challenge level
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Weekly Problem 43 - 2015
Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?
Test Scores
problem

Test scores

Age
14 to 16
Challenge level
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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?
Baby Boom
problem

Baby boom

Age
14 to 16
Challenge level
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Which of the cities shown had the largest percentage increase in population?
Tennis Club
problem

Tennis club

Age
14 to 16
Challenge level
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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
problem

The Grand Old Duke of York

Age
14 to 16
Challenge level
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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?

Pied Piper
problem

Pied Piper

Age
14 to 16
Challenge level
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How many rats did the Pied Piper catch?

Porridge
problem

Porridge

Age
14 to 16
Challenge level
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To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?
Entrance Exam
problem

Entrance exam

Age
14 to 16
Challenge level
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Dean finishes his exam strongly. Can you work out how many questions are on the paper if he gets an average of 80%?
Meeting Point
problem

Meeting point

Age
14 to 16
Challenge level
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Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?
Petrol Station
problem

Petrol station

Age
14 to 16
Challenge level
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Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?
Solitare
problem

Solitare

Age
14 to 16
Challenge level
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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 Unchanged
problem

Percentage unchanged

Age
14 to 16
Challenge level
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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
problem

Washing-up

Age
14 to 16
Challenge level
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What fraction of customers buy Kleenz after the advertising campaign?
Breakfast Time
problem

Breakfast time

Age
14 to 16
Challenge level
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Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?
Itchy's Fleas
problem

Itchy's fleas

Age
14 to 16
Challenge level
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Itchy the dog has a million fleas. How many fleas might his shampoo kill?
Percentage Swap
problem

Percentage swap

Age
14 to 16
Challenge level
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What is 50% of 2007 plus 2007% of 50?
Recurring Mean
problem

Recurring mean

Age
14 to 16
Challenge level
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What is the mean of 1.2 recurring and 2.1 recurring?
Placeholder: several colourful numbers
problem

Coal truck

Age
14 to 16
Challenge level
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What percentage of the truck's final mass is coal?
Placeholder: several colourful numbers
problem

Pineapple juice

Age
14 to 16
Challenge level
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What percentage of this orange drink is juice?
Fractions of 1000
problem

Fractions of 1000

Age
14 to 16
Challenge level
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Find a simple way to compute this long fraction.
Bargain
problem

Bargain

Age
14 to 16
Challenge level
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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
problem

2011 digits

Age
14 to 16
Challenge level
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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
problem

Producing an integer

Age
14 to 16
Challenge level
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Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?
Squeezed In
problem

Squeezed in

Age
14 to 16
Challenge level
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Weekly Problem 9 - 2017
What integer x makes x/9 lie between 71/7 and 113/11?
Antiques Roadshow
problem

Antiques roadshow

Age
14 to 16
Challenge level
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Last year, on the television programme Antiques Roadshow... work out the approximate profit.
Elephants and geese
problem

Elephants and geese

Age
14 to 16
Challenge level
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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
problem

The property market

Age
14 to 16
Challenge level
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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?