# Browsing category fractions

## Ask Uncle Colin: My partial fractions decompose funny

Dear Uncle Colin, I recently had to decompose $\frac{3+4p}{9p^2 - 16}$ into partial fractions, and ended up with $\frac{\frac{25}{8}}{p-\frac{4}{3}} + \frac{\frac{7}{8}}{p-\frac{4}{3}}$. Apparently, that's wrong, but I don't see why! -- Drat! Everything Came Out Messy. Perhaps Other Solution Essential. Hi, there, DECOMPOSE, and thanks for your message - and your

## Ask Uncle Colin; A variable fraction

Dear Uncle Colin, I have a fraction, $\frac{x^2-x}{x-1}$, and I want to cancel it down to $x$ - but I'm not sure those are the same. Are they? - Got A Lot Of Interesting Sums Hi, GALOIS, and thanks for your message! The short answer is, yes and no. Everywhere

## Fractions that generate Pythagorean Triples

An interesting tweet, some time ago, from @RJS2212: Two unit fractions where denominators differ by 2Add fractionsNumerator & denominator of the sum are two smaller numbers of Pythag triple — Robert J Smith (@RJS2212) May 30, 2016 And of course, you wonder two things: a) why does it work, and

## On recurring decimals

It's encouraging to see a few less-predictable questions coming up in the new GCSE and A-level specifications. @mathsjem highlighted an especially nice GCSE one: Question 26 from yesterday's Edexcel Methods 2 GCSE paper. Helpful for revising recurring decimals. pic.twitter.com/78BghgBSvE — Jo Morgan (@mathsjem) June 17, 2016 This is unusual more

## Ask Uncle Colin: How do I multiply mixed fractions?

Dear Uncle Colin, I'm OK at multiplying simple fractions by numbers and fractions by each other, but I don't understand how to multiply mixed fractions together. Help! -- Variations In Numerators Can Upset Learners Understanding Maths Hello VINCULUM1 ! I think I'm on record as saying that mixed fraction are

## The Mathematical Ninja and the Nineteenths

"Look," said the student, "we all know how this goes down. A nasty-looking fraction comes out of the sum, I reach for the calculator, you commit some act of exaggerated violence and tell me how you, o wondrous one, can do it in your head." "You're not as dumb as

## The Bigger Fraction

Some while back, Ben Orlin of the brilliant Maths With Bad Drawings blog posted a puzzle he'd set for some eleven-year-olds: Which is larger, $\frac{3997}{4001}$ or $\frac{4996}{5001}$? Hint: they differ by less than 0.000 000 05. He goes on to explain how he solved it (by considering the difference between

## The Mathematical Ninja and the twenty-sixths

The Mathematical Ninja played an implausible trick shot, not only removing himself from a cleverly-plotted snooker, but potting a red his student had presumed safe and setting himself up on the black. Again. "One!" he said, brightly, and put some chalk on the end of his cue. The student sighed.

## Ask Uncle Colin: simplifying fractions

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I'm having trouble cancelling fractions -- in

## Using continued fractions to generate rational approximations

A redditor asks: How would I find a good rational approximation to something like $\log_{10}(7)$? The Mathematical Ninja mutters 0.85 under his breath, as a matter of course, reasoning that $\log_{10}(7) \approx \log_{10}\left(\sqrt{ \frac {10^2 }{2} } \right)$, although my calculator says 0.845098, so he's off by about 0.6%. However,