Does $5\sqrt{5}\div5\sqrt{5}$ equal 5 or 1

Question

Does $5\sqrt{5}\div5\sqrt{5}$ equal $5$ or $1$.

I think it is $1$ but I just want to check I have not missed anything.

Answer 1

At face-value, it's ambiguous. But there's a convention that says evaluate from left to right, so the parens should be

$$((5\sqrt{5})\div 5)\sqrt{5} =5.$$

Answer 2

Writing $5\cdot\sqrt5 \div 5\cdot \sqrt 5$ would be ambiguous -- it wouldn't be clear whether you mean $((5\cdot\sqrt5) \div 5)\cdot 5$ or $(5\cdot\sqrt5) \div (5\cdot \sqrt5)$.

However, when the multiplications are indicated just by placing expressions next to each other, they almost always bind tighter than operations that are notated with a visible symbol. So if someone writes $5\sqrt 5 \div 5\sqrt 5$ the probability is overwhelming that they mean $\frac{5\sqrt5}{5\sqrt 5}$, which is of course $1$.

(Or possibly they're wiseguys who are planning to select the opposite interpretation of whatever you choose. Writing $\div$ instead of $/$ or a horizontal fraction bar suggests they are not much used to mathematical conventions).