Fraction fun « Wild About Math!

27Mar/098

Fraction fun

Here's an interesting equation:

[pmath size=12] 50 1/2 + 49 38/76 = 100 [/pmath]

It's interesting because the left side of the equation uses each of the digits between 0 and 9 exactly once.

Here's another example:

[pmath size=12] 97 30/45 + 2 6/18 = 100 [/pmath]

Can you find other such equations where the left side has whole numbers and fractions which sum to 100?

For those of you so inclined, can you get a computer to find all solutions?

Loai Najati
March 30th, 2009 - 09:57

Amazing!. Thanks
Ishita
March 30th, 2009 - 16:51

This a great problem for after any test. Thanks
Quan
March 31st, 2009 - 11:17

can’t wait to try this!
Jonathan
April 4th, 2009 - 13:32

I’m fairly confident that there are many solutions.

if this: 21/3 + 8 + 4 + 7 + 60 + 5 + 9

is allowed.
Michael Croucher
April 14th, 2009 - 09:04

Hi Sol

I liked the problem so had a crack at a computer solution.

http://www.walkingrandomly.com/?p=1019

580 (I think) solutions if you keep to only 2 integer terms and 2 fraction terms as you did in your examples.
Anthony
April 16th, 2009 - 05:25

I thought I was pretty reasonable at maths before I saw this blog. I think I need to go back to school.
Annette
March 1st, 2011 - 16:31

I understand this post is years later (literally), but for class work in my Teaching Middle Grade Mathematics, we needed to comment on a post about fractions. Where did the notion for this patter come from?
Alexander Bogomolny
March 9th, 2011 - 21:50

Have you seen this: 1 = 148/296 + 35/70?

Simpler ones at

http://www.cut-the-knot.org/do_you_know/digits.shtml