# 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 VINCULUM ((It’s the line between the numerator and denominator, just so we’re clear)) ! 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!