Fractions, Decimals and Percentages - Short Problems

problem

Jacob's Flock

Age

11 to 14

Challenge level

How many sheep are in Jacob's flock?

problem

Bouncing ball

Age

11 to 14

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.

problem

Information Display

Age

11 to 14

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?

problem

Mean Sequence

Age

11 to 14

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?

problem

Better Spelling

Age

11 to 14

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.

problem

Valuable Percentages

Age

11 to 14

Challenge level

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

problem

Ordering Fractions

Age

11 to 14

Challenge level

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

problem

Multiplication Magic Square

Age

11 to 14

Challenge level

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

Which of these fractions is the largest?

problem

Tommy's Tankard

Age

11 to 14

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?

problem

Smashing Time

Age

11 to 14

Challenge level

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

problem

Talulah's Tulips

Age

11 to 14

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?

problem

Percentage Mad

Age

11 to 14

Challenge level

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

problem

Smallest Fraction

Age

11 to 14

Challenge level

Which of these is the smallest?

problem

Charlie's money

Age

11 to 14

Challenge level

How much money did Charlie have to begin with?

problem

Halfway

Age

11 to 14

Challenge level

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

problem

Pride of Place

Age

11 to 14

Challenge level

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

problem

between a sixth and a twelfth

Age

11 to 14

Challenge level

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

problem

Magical Products

Age

11 to 14

Challenge level

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

problem

Three Blind Mice

Age

11 to 14

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?

problem

Second Half Score

Age

11 to 14

Challenge level

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

problem

Peanut Harvest

Age

11 to 14

Challenge level

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

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

problem

Slightly Outnumbered

Age

11 to 14

Challenge level

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

problem

How Shady?

Age

11 to 14

Challenge level

What fraction of this triangle is shaded?

problem

Too Close to Call

Age

11 to 14

Challenge level

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

problem

Porridge

Age

14 to 16

Challenge level

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

problem

Entrance Exam

Age

14 to 16

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%?

problem

Meeting Point

Age

14 to 16

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?

problem

Petrol Station

Age

14 to 16

Challenge level

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

problem

A Drink of Water

Age

14 to 16

Challenge level

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

problem

Test Scores

Age

14 to 16

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?

problem

Baby Boom

Age

14 to 16

Challenge level

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

problem

Tennis Club

Age

14 to 16

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?

problem

The Grand Old Duke of York

Age

14 to 16

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?

problem

Pied Piper

Age

14 to 16

Challenge level

How many rats did the Pied Piper catch?

problem

Percentage Swap

Age

14 to 16

Challenge level

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

problem

Recurring Mean

Age

14 to 16

Challenge level

What is the mean of 1.2 recurring and 2.1 recurring?

problem

Coal truck

Age

14 to 16

Challenge level

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

problem

Pineapple juice

Age

14 to 16

Challenge level

What percentage of this orange drink is juice?

problem

Fractions of 1000

Age

14 to 16

Challenge level

Find a simple way to compute this long fraction.

problem

Bargain

Age

14 to 16

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?

problem

2011 Digits

Age

14 to 16

Challenge level

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

problem

Solitare

Age

14 to 16

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%?

problem

Percentage Unchanged

Age

14 to 16

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 ?

problem

Washing-Up

Age

14 to 16

Challenge level

What fraction of customers buy Kleenz after the advertising campaign?

problem

Breakfast Time

Age

14 to 16

Challenge level

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

problem

Itchy's Fleas

Age

14 to 16

Challenge level

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

problem

Percentage of a Quarter

Age

14 to 16

Challenge level

What percentage of a quarter is a fifth?

problem

Antiques Roadshow

Age

14 to 16

Challenge level

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

problem

Elephants and geese

Age

14 to 16

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?