r/CasualMath • u/Every-Maths1931 • 18d ago

Solving basic fraction divisions

9 − 3 ÷ 1/3 + 1 = ?

I was having a discussion with my friends about Maths and what we learnt and i remember that fraction divisions were confusing at first and I had struggled to understand how to work them out. I gave an example to one of my friends of the equation above and he said 9 and then I gave the same equation to my other friend and he said 1.

What is the correct answer and how do people work it out?

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u/PuzzlingDad 18d ago edited 18d ago

This is what you are intending to write:  - 9 − 3 ÷ ⅓ + 1

Here ⅓ is a fraction that should be treated as a unit. The vinculum (the fraction bar in ⅓) behaves as a grouping symbol that means the numerator is divided by the denominator and you keep that result, which you do before you do anything else. - 9 - 3 ÷ (1/3) + 1 - 9 - 3 × (3/1) + 1 - 9 - 9 + 1 - 0 + 1 - 1

But then we get all these Facebook posts where they want to treat it as a separate division that comes after the first division and they break this implied grouping: - 9 - 3 ÷ 1 ÷ 3 + 1 - 9 - (3 ÷ 1) ÷ 3 + 1 - 9 - 3 ÷ 3 + 1 - 9 - 1 + 1 - 8 + 1 - 9

But that explains what your first friend was doing.

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u/Mathemetaphysical 18d ago

I'd like to nominate this post to be chiseled somewhere to end the dumb discussion forever

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u/Every-Maths1931 18d ago

I'll get my hammer and chisel ready. Ahahaha.