Ask Uncle Colin: How do I multiply mixed 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 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 embodiment of pure evil, but I'll repeat it here for good measure: they take the worst bits of decimals, fractions and notation, and combine them together into one smelly package.

There are two possible ways I'd recommend to work out something like $3 \frac{1}{7} \times 2 \frac{2}{3}$:

First option, turn them both into improper (top-heavy) fractions: $3\frac{1}{7} = \frac{22}{7}$ and $2 \frac{2}{3} = \frac{8}{3}$. You can then multiply as normal to get $\frac{22 \times 8}{7 \times 3} = \frac{176}{21}$. You could turn that back into a mixed number (it's $8 \frac{8}{21}$).

Second option, which I don't recommend so strongly, is to treat the mixed number like a bracket: $3\frac{1}{7} \times 2 \frac{2}{3}$ is the same thing as $\left(3 + \frac{1}{7}\right)\left(2 + \frac{2}{3}\right)$. You can expand this like you would with algebraic factors to get $6 + \frac{2}{7} + 2 + \frac{2}{21} = 8 + \frac{8}{21}$, but I don't think that saves any work.

Hope that helps!

-- Uncle Colin

* Edited 2016-07-27 to fix LaTeX. Thanks, @dragon_dodo!


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.

  1. It's the line between the numerator and denominator, just so we're clear []


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