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 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

Hi, FACTOR!

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

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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