# Fractions, Decimals, Percentages and Ratio - Short Problems

### Anulus Area

##### Stage: 3 and 4 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?

### Producing an Integer

##### Stage: 3 and 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?

### Inspector Remorse

##### Stage: 3 Short Challenge Level:

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

##### Stage: 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?

### Off the Cuff

##### Stage: 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?

### Too Close to Call

##### Stage: 3 Short Challenge Level:

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

### Farthest Fraction

##### Stage: 2 and 3 Short Challenge Level:

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

### Televisual Technology

##### Stage: 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?

### Smashing Time

##### Stage: 2 and 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?

### Middle of the Fraction Road

##### Stage: 2 and 3 Short Challenge Level:

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

### A Leg to Stand On

##### Stage: 3 Short Challenge Level:

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

### Baby Boom

##### Stage: 3 Short Challenge Level:

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

### Marathon Mission

##### Stage: 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?

##### Stage: 3 Short Challenge Level:

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

### Fractions of Fractions

##### Stage: 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?

### Dividing by a Half

##### Stage: 2 and 3 Short Challenge Level:

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

### Weekly Problem 7 - 2008

##### Stage: 3 and 4 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?

### Weekly Problem 12 - 2008

##### Stage: 3 and 4 Challenge Level:

A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

### Weekly Problem 32 - 2008

##### Stage: 3 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?

### Weekly Problem 37 - 2008

##### Stage: 3 Challenge Level:

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?

### Weekly Problem 44 - 2008

##### Stage: 3 Short Challenge Level:

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?

### Weekly Problem 52 - 2008

##### Stage: 3 Short Challenge Level:

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?

### Slightly Outnumbered

##### Stage: 2 and 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?

### Better Spelling

##### Stage: 2 and 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.

### Valuable Percentages

##### Stage: 2 and 3 Short Challenge Level:

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

### Half Way

##### Stage: 3 Short Challenge Level:

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

### Shepherd's Flock

##### Stage: 2 and 3 Short Challenge Level:

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

### Pride of Place

##### Stage: 3 Short Challenge Level:

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

### Cover-up

##### Stage: 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?

### Fractions of 1000

##### Stage: 3 and 4 Short Challenge Level:

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

### Petrol Station

##### Stage: 2 and 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?

### Magical Products

##### Stage: 2 and 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?

### Three Blind Mice

##### Stage: 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?

### Bargain

##### Stage: 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?

### 2011 Digits

##### Stage: 3 and 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?

### Spider Solitare

##### Stage: 3 and 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%?

### Cubic Fractions

##### Stage: 3 and 4 Short Challenge Level:

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

### Multiplication Magic Square

##### Stage: 3 Short Challenge Level:

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

### A Drink of Water

##### Stage: 3 and 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?

### Test Scores

##### Stage: 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?

### Peter Piper

##### Stage: 3 Short Challenge Level:

Weekly Problem 21 - 2016
Peter Piper picked a peck of pickled peppers. How many more pecks must Peter Piper pick to fill a barrel?

### Washing-up

##### Stage: 3 Short Challenge Level:

Weekly Problem 34 - 2016
A survey for washing-up liquid revealed that 2/3 of customers bought Jinx, and 1/3 of customers bought Kleenz. After an advertising campaign, what fraction of customers buy Kleenz?

### Square Percentage

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 36 - 2016
What percentage of the integers between 1 and 10,000 are square numbers?

### Squares in a Square

##### Stage: 3 Short Challenge Level:

Weekly Problem 43 - 2016
In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

### Second Half Score

##### Stage: 3 Short Challenge Level:

Weekly Problem 48 - 2016
Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?

### Breakfast Time

##### Stage: 3 Short Challenge Level:

Weekly Problem 49 - 2016
Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?

### Traffic Jam

##### Stage: 3 Short Challenge Level:

Weekly Problem 1 - 2017
Yesterday evening, Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced compared to normal?

### Printer Ink

##### Stage: 3 Short Challenge Level:

Weekly Problem 2 - 2017
A small ink cartridge has enough ink to print 600 pages. How many pages can be printed using a large ink cartridge.

### Tommy's Tankard

##### Stage: 3 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?

### Talulah's Tulips

##### Stage: 3 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?

### A Classy Ratio

##### Stage: 3 Short Challenge Level:

Weekly Problem 12 - 2017
There are six more girls than boys in Miss Spelling's class of 24 pupils. What is the ratio of girls to boys in the class?

### Star in a Hexagon

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 20 - 2017
The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?

### Itchy's Fleas

##### Stage: 3 Short Challenge Level:

Weekly Problem 32 - 2017
Itchy has a million fleas. His anti-flea leaves no more than 1% of the original fleas after use. What is the least number of fleas that the shampoo will remove?

### Athletics Club

##### Stage: 3 Short Challenge Level:

Weekly Problem 7 - 2017
An athletics club has girl, boy and adult members in the ratio 3:4:9. If there are 16 more adult members than junior members, how many members does the club have?

### Squeezed In

##### Stage: 3 Short Challenge Level:

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

### The Grand Old Duke of York

##### Stage: 3 Short Challenge Level:

Weekly Problem 44 - 2017
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?

### How Many Swimmers

##### Stage: 3 Short Challenge Level:

Weekly Problem 46 - 2017
Given the ratios of junior to senior and senior to veteran members, can you work out what the smallest possible number of members in a swimming club is?

### Percentage of a Quarter

##### Stage: 3 Short Challenge Level:

Weekly Problem 50 - 2017
What percentage of a quarter is a fifth?