A unit fraction is one where the numerator is 1 and the denominator is some other whole number. There are times when such fractions continue to be useful, especially with non-decimal units of measurement such as those based on 12, 24 or 60 units. Fibonacci shows how to handle both decimal fractions and sums of unit fractions.

For example, the circle to the left is subdivided in such a way to show that one-half is equal to a third plus a sixth. Alternatively, the other half is divided into 1/3 plus 1/9 and 1/18. Without any further calculations, the diagram itself also shows that we can express 1/3 as 1/6 + 1/9 + 1/18. And finally, we have 2/3 = 1/2 + 1/9 + 1/18.

**The Question**Let us take the following three numbers from the Fibonacci sequence: 21, 34, 55. Below are two fractions formed from adjacent terms, both expressed as sums of unit fractions. With a, b, c and d being whole numbers, and a < b < c < d, find the value of (a + b + c + d). As always, you must show a valid method together with the correct answer.

During this week, we have barely scratched the surface of Fibonacci's work in mathematics. Although we have concentrated on Fibonacci’s practical and mercantile mathematics, he also wrote on number theory and geometry. We shall return to explore some of these other works in the future.

Click banner for details. |

**How to Enter****Send your complete solution by email to [competition closed - email removed].**This email address shall be removed after the competition closes to avoid spam.

**This PMQ8 competition closes on Sunday 3 March at 23:59 GMT**.

**The Prize****The prizes for this PMQ8 are 3 free places in our Online Classroom for 2 months.**The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received.

**Quick Rules****Look at the expanded rules on our PMQ page.**

Anybody can enter our Prize Maths Quiz; adults and students.

Use the official server clock in the right column to avoid late entries.

All emails and email addresses sent to us will be deleted after the winners have been processed.

DO NOT submit your entries to the comments section at the bottom of this post.

You CAN discuss it there but you must email us to enter the competition.

We adhere to COPPA guidelines regarding children's online safety and security.

Enjoy the challenge!

**Send us your solution! You can't win if you don't participate.**

Then tell your friends!

## No comments:

## Post a Comment