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 and Uncle Colin will do what he can.

Dear Uncle Colin,

I'm having trouble cancelling fractions -- in a calculator paper, it's easy to turn $\frac{76}{95}$ into $\frac{4}{5}$, but I can't see how to do it on paper.

I don't know my 19 times table! Is there something wrong with me?

-- Fractions And Cancelling Test Our Resilience


First up, rest assured: there's nothing abnormal in struggling to cancel down $\frac{76}{95}$, even if some superhumans know their nineteen times table!

You can do it without the calculator, though -- all you need to do is factorise the two numbers!

The top (76) is obviously even -- so it's a multiple of 2; in fact, it's 2 × 38. Thirty-eight is also even, so you can split it up further -- $76 = 2 \times 2 \times 19$.

The same idea on the bottom: it's a multiple of 5, so you can turn it into $5 \times 19$.

Aha! A common factor of 19, top and bottom, so you can remove it -- leaving $2 \times 2 = 4$ on top and just $5$ on the bottom.

It's a good idea to remember your simple divisibility rules:

  • If a number ends in 2, 4, 6, 8 or 0, it's a multiple of 2
  • If a number ends in 5 or 0, it's a multiple of 5;
  • If you add up the digits in a number and get a multiple of 3, the original number is a multiple of 3

(There are other rules for other factors, but they're more involved and rarely necessary).

One bonus tip: if you find an unusual factor (such as 19) of one part of the fraction, it's worth checking if it's a factor of the other part, too. It isn't always, but it's a fair bet.

-- Uncle Colin

* Edited 2015-09-26 to fix HTML


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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