# Fractions, Decimals, Percentages and Ratio - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Fractions, Decimals Percentages and Ratio.

### Restful Sundays

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 17 - 2006
Granny says she is 84 years old, not counting her Sundays. How old is she?

### Smashing Time

##### KS 2 & 3 Short Challenge Level:

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

### Slightly Outnumbered

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 3 - 2010
If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?

### Dividing by a Half

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 46 - 2013
What is the value of 3 divided by one half?

### Middle of the Fraction Road

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 29 - 2012
Which fraction is halfway between one quarter and one eigth?

### Better Spelling

##### KS 2 & 3 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.

### Petrol Station

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 15 - 2011
Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?

### Valuable Percentages

##### KS 2 & 3 Short Challenge Level:

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

### Magical Products

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 9 - 2013
Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

### Farthest Fraction

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 26 - 2012
Which of these fractions is the largest?

### Shepherd's Flock

##### KS 2 & 3 Short Challenge Level:

Weekly Problem 26 - 2010
Does Joseph have too many sheep in his flock...

### Question Setters

##### KS 3 Short Challenge Level:

Weekly Problem 44 - 2008
John, Peter, Rudolf, Susie and Tony decide to set some questions for the Schools Mathematical Challenge. Can you work out how long in total they spend setting questions?

##### KS 3 Short Challenge Level:

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

### Bargain

##### KS 3 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?

### Televisual Technology

##### KS 3 Short Challenge Level:

Weekly Problem 27 - 2012
Television screens have changed from the traditional 4:3 to widescreen 16:9. If a new television and an old television have the same area, what is the ratio of their widths?

### Pride of Place

##### KS 3 Short Challenge Level:

Weekly Problem 47 - 2010
Two fractions have been placed on a number line. Where should another fraction be placed?

### Tyre Wear

##### KS 3 Short Challenge Level:

Weekly Problem 52 - 2008
A car with 5 tyres (four road tyres and a spare) travelled 30,000 km. All 5 tyres were used equally. How many kilometres' wear did each tyre receive?

### Cover-up

##### KS 3 Short Challenge Level:

Weekly Problem 49 - 2010
When I place a triangle over a small square, or cover a larger square with the same triangle, a certain proportion of each is covered. What is the area of the triangle?

### Chocolate Multipliers

##### KS 3 Short Challenge Level:

Weekly Problem 23 - 2006
Can you work out how many times more chocolate Peg has then Meg?

### Inspector Remorse

##### KS 3 Short Challenge Level:

Weekly Problem 49 - 2011
How long will it take Inspector Remorse to crack this crime spree?

##### KS 3 Short Challenge Level:

Weekly Problem 10 - 2012
If you know how long Meg's shadow is, can you work out how long the shadow is when she stands on her brother's shoulders?

### Tennis Club

##### KS 3 Short Challenge Level:

Weekly Problem 6 - 2007
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?

### Information Display

##### KS 3 Short Challenge Level:

Weekly Problem 7 - 2008
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?

### A Leg to Stand On

##### KS 3 Short Challenge Level:

Weekly Problem 30 - 2012
Can you work out the number of chairs at a cafe from the number of legs?

### Off the Cuff

##### KS 3 Short Challenge Level:

Weekly Problem 23 - 2012
Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?

### Multiplication Magic Square

##### KS 3 Short Challenge Level:

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

### Meeting Point

##### KS 3 Short Challenge Level:

Weekly Problem 32 - 2008
Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

### Baby Boom

##### KS 3 Short Challenge Level:

Weekly Problem 25 - 2012
Which of the cities shown had the largest percentage increase in population?

### Family Fortune

##### KS 3 Short Challenge Level:

Weekly Problem 8 - 2007
If three brothers will get £20 more if they do not share their money with their sister. How much money is there?

### Too Close to Call

##### KS 3 Short Challenge Level:

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

### Half Way

##### KS 3 Short Challenge Level:

Weekly Problem 24 - 2010
Can you find a number that is half way between these two fractions?

### Flapjack

##### KS 3 Short Challenge Level:

Weekly Problem 37 - 2008
A recipe for flapjacks calls for a certain quantity of butter, sugar and oats. Given the amount of these ingredients I have, how many flapjacks can I make?

### Marathon Mission

##### KS 3 Short Challenge Level:

Weekly Problem 33 - 2012
Minnie trained more for the London Marathon this year, so her speed increased. By what percentage did her time decrease?

### Three Blind Mice

##### KS 3 Short Challenge Level:

Weekly Problem 10 - 2013
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?

### Porridge

##### KS 3 Short Challenge Level:

Weekly Problem 43 - 2006
To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?

### Test Scores

##### KS 3 Short Challenge Level:

Weekly Problem 10 - 2016
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?

### Fractions of Fractions

##### KS 3 Short Challenge Level:

Weekly Problem 44 - 2013
If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

### Pied Piper

##### KS 3 Short Challenge Level:

Weekly Problem 7 - 2007
How many rats did the Pied Piper catch?

### Painting the Forth Bridge

##### KS 3 Short Challenge Level:

Weekly Problem 14 - 2006
Given the rates at which men can paint, how long will it take them to paint the Forth Bridge?

### Anulus Area

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 38 - 2011
Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

### Percentage Swap

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 47 - 2007
What is 50% of 2007 plus 2007% of 50?

### Recurring Mean

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 49 - 2007
What is the mean of 1.2 recurring and 2.1 recurring?

### Spider Solitare

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 45 - 2014
After playing 500 games, my success rate at Spider Solitare is 49%. How many games do I need to win to increase my success rate to 50%?

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 51 - 2007
Last year, on the television programme Antiques Roadshow... work out the approximate profit.

### Fractions of 1000

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 50 - 2010
Find a simple way to compute this long fraction.

### Cubic Fractions

##### KS 3 & 4 Short Challenge Level:

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

### Ratio Riddle

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 8 - 2006
Can you work out the ratio $b:c$ given the ratios $a:b$ and $a:c$.

### A Drink of Water

##### KS 3 & 4 Short Challenge Level:

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

### Producing an Integer

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 46 - 2011
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

### 2011 Digits

##### KS 3 & 4 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?

### Antifreeze

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 4 - 2007
How much more antifreeze is needed to make the proportion 30%?

### Flower Show

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 7 - 2006
It takes four gardeners four hours to dig four circular flower beds, each of diameter 4 metres. How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?