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.

Information Display

Age 11 to 14 Short Challenge Level:

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

Age 11 to 14 Short Challenge Level:

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

Age 11 to 14 Short Challenge Level:

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

Jacob's Flock

Age 11 to 14 Short Challenge Level:

How many sheep are in Jacob's flock?

Farthest Fraction

Age 11 to 14 Short Challenge Level:

Which of these fractions is the largest?

Tommy's Tankard

Age 11 to 14 Short Challenge Level:

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

Age 11 to 14 Short Challenge Level:

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

Smashing Time

Age 11 to 14 Short Challenge Level:

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

Talulah's Tulips

Age 11 to 14 Short Challenge Level:

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

Age 11 to 14 Short Challenge Level:

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

Age 11 to 14 Short Challenge Level:

Weekly Problem 23 - 2010
These numbers have been written as percentages. Can you work out which has the greatest value?

Bouncing Ball

Age 11 to 14 Short Challenge Level:

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

Age 11 to 14 Short Challenge Level:

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

Pride of Place

Age 11 to 14 Short Challenge Level:

Two fractions have been placed on a number line. Where should another fraction be placed?

Second Half Score

Age 11 to 14 Short Challenge Level:

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

Age 11 to 14 Short Challenge Level:

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

Magical Products

Age 11 to 14 Short Challenge Level:

Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

Smallest Fraction

Age 11 to 14 Short Challenge Level:

Which of these is the smallest?

Three Blind Mice

Age 11 to 14 Short Challenge Level:

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?

Charlie's Money

Age 11 to 14 Short Challenge Level:

How much money did Charlie have to begin with?

Halfway

Age 11 to 14 Short Challenge Level:

Can you find a number that is halfway between two fractions?

Tricky Fractions

Age 11 to 14 Short Challenge Level:

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

Too Close to Call

Age 11 to 14 Short Challenge Level:

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

Slightly Outnumbered

Age 11 to 14 Short Challenge Level:

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

How Shady?

Age 11 to 14 Short Challenge Level:

What fraction of this triangle is shaded?

Peanut Harvest

Age 11 to 14 Short Challenge Level:

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

Tennis Club

Age 14 to 16 Short Challenge Level:

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

Age 14 to 16 Short Challenge Level:

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

Age 14 to 16 Short Challenge Level:

Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

Pied Piper

Age 14 to 16 Short Challenge Level:

How many rats did the Pied Piper catch?

Porridge

Age 14 to 16 Short Challenge Level:

To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?

Petrol Station

Age 14 to 16 Short Challenge Level:

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

A Drink of Water

Age 14 to 16 Short Challenge Level:

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

Entrance Exam

Age 14 to 16 Short Challenge Level:

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

Age 14 to 16 Short Challenge Level:

Which of the cities shown had the largest percentage increase in population?

Test Scores

Age 14 to 16 Short Challenge Level:

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?

Percentage Unchanged

Age 14 to 16 Short Challenge Level:

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

Age 14 to 16 Short Challenge Level:

What fraction of customers buy Kleenz after the advertising campaign?

2011 Digits

Age 14 to 16 Short Challenge Level:

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

Pineapple Juice

Age 14 to 16 Short Challenge Level:

What percentage of this orange drink is juice?

Solitare

Age 14 to 16 Short Challenge Level:

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 of a Quarter

Age 14 to 16 Short Challenge Level:

What percentage of a quarter is a fifth?

Fractions of 1000

Age 14 to 16 Short Challenge Level:

Find a simple way to compute this long fraction.

Breakfast Time

Age 14 to 16 Short Challenge Level:

Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?

Percentage Swap

Age 14 to 16 Short Challenge Level:

What is 50% of 2007 plus 2007% of 50?

Recurring Mean

Age 14 to 16 Short Challenge Level:

What is the mean of 1.2 recurring and 2.1 recurring?

Itchy's Fleas

Age 14 to 16 Short Challenge Level:

Itchy the dog has a million fleas. How many fleas might his shampoo kill?

Bargain

Age 14 to 16 Short Challenge Level:

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

Coal Truck

Age 14 to 16 Short Challenge Level:

What percentage of the truck's final mass is coal?

Producing an Integer

Age 14 to 16 Short Challenge Level:

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Elephants and Geese

Age 14 to 16 Short Challenge Level:

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

Age 14 to 16 Short Challenge Level:

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?

Antiques Roadshow

Age 14 to 16 Short Challenge Level:

Last year, on the television programme Antiques Roadshow... work out the approximate profit.

Squeezed In

Age 14 to 16 Short Challenge Level:

Weekly Problem 9 - 2017
What integer x makes x/9 lie between 71/7 and 113/11?