Fractions - Short Problems

A collection of short Stage 3 and 4 problems on fractions, decimals, percentages and ratio



Weekly Problem 37 - 2011

Challenge Level: Challenge Level:1

Rotating a pencil twice about two different points gives surprising results...

Weekly Problem 38 - 2011

Challenge Level: Challenge Level:1

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

Weekly Problem 49 - 2011

Challenge Level: Challenge Level:1

How long will it take Inspector Remorse to crack this crime spree?

Weekly Problem 7 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

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: Challenge Level:1

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: Challenge Level:1

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: Challenge Level:1

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: Challenge Level:1

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: Challenge Level:1

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?

Weekly Problem 3 - 2010

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 23 - 2010

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 24 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

Can you find a number that is half way between these two fractions?

Weekly Problem 26 - 2010

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Does Joseph have too many sheep in his flock...

Weekly Problem 47 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 49 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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?

Weekly Problem 50 - 2010

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Find a simple way to compute this long fraction.

Weekly Problem 15 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 27 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Pizza, Indian or Chinese takeaway. Each teenager from a class only likes two of these, but can you work which two?

Weekly Problem 28 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.

Weekly Problem 10 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 10 - 2014

Weekly Problem 45 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 45 - 2014