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# 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.

### Mean Sequence

### Ordering Fractions

### Tommy's Tankard

### Multiplication Magic Square

### Smashing Time

### Talulah's Tulips

### Better Spelling

### Valuable Percentages

### Bouncing Ball

### Percentage Mad

### Information Display

### Second Half Score

### Between a Sixth and a Twelfth

### Magical Products

### Three Blind Mice

### Halfway

### Pride of Place

### Too Close to Call

### Slightly Outnumbered

### Peanut Harvest

### Tricky Fractions

### Meeting Point

### Porridge

### Petrol Station

### A Drink of Water

### Entrance Exam

### Baby Boom

### Test Scores

### Tennis Club

### The Grand Old Duke of York

### Solitare

### Fractions of 1000

### Breakfast Time

### Recurring Mean

### Itchy's Fleas

### Bargain

### Percentage Unchanged

### Washing-up

### 2011 Digits

### Producing an Integer

### Elephants and Geese

### The Property Market

### Antiques Roadshow

### Squeezed In

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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.

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

Weekly Problem 46 - 2014

Which of these fractions has greatest value?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

Weekly Problem 32 - 2015

Can you work out the missing numbers in this multiplication magic square?

Age 11 to 14

ShortChallenge Level

Weekly Problem 58 - 2012

Once granny has smashed some of her cups and saucers, how many cups are now without saucers?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge 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.

Age 11 to 14

ShortChallenge Level

Weekly Problem 23 - 2010

These numbers have been written as percentages. Can you work out which has the greatest value?

Age 11 to 14

ShortChallenge 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.

Age 11 to 14

ShortChallenge Level

Weekly Problem 43 - 2013

What is 20% of 30% of 40% of Â£50?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

Weekly Problem 24 - 2012

Can you put these very close fractions into order?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

Weekly Problem 43 - 2015

Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?

Age 14 to 16

ShortChallenge Level

Dean finishes his exam strongly. Can you work out how many questions are on the paper if he gets an average of 80%?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge 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%?

Age 14 to 16

ShortChallenge Level

Find a simple way to compute this long fraction.

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

What is the mean of 1.2 recurring and 2.1 recurring?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

Weekly Problem 11 - 2013

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

Age 14 to 16

ShortChallenge Level

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

Age 14 to 16

ShortChallenge Level

What fraction of customers buy Kleenz after the advertising campaign?

Age 14 to 16

ShortChallenge Level

Weekly Problem 10 - 2014

What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

Weekly Problem 9 - 2017

What integer x makes x/9 lie between 71/7 and 113/11?