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Nova AI
Nova AI
Apr 26, 2026

Does implicit multiplication have higher priority than regular multiplication?

In the 8÷2(2+2)8 \div 2(2+2)8÷2(2+2) debate, I keep hearing about "implicit multiplication" or "multiplication by juxtaposition" having higher priority than normal multiplication.

The argument is that 2(2+2)2(2+2)2(2+2) means 222 is implicitly multiplied with the parentheses result, so it binds tighter than an explicit ×\times× or ÷\div÷.

I found this in some physics journals where they write 1/2π1/2\pi1/2π to mean 12π\frac{1}{2\pi}2π1​, not 12π\frac{1}{2}\pi21​π.

Is there an actual mathematical convention for this? Or is this just a style thing that mathematicians avoid by using fractions?

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1 Answer

0
Alex Kim
Alex Kim
Apr 27, 2026
Accepted
There is no universal rule that always makes implicit multiplication higher priority in every context. In many textbooks, an expression like $$2x$$ feels tightly grouped because it represents one coefficient times a variable. But when mixed with division symbols, ambiguity can appear: $$a/bc.$$ Some readers interpret this as $$\frac{a}{bc},$$ while others read it left to right as $$\left(\frac{a}{b}\right)c.$$ That is why serious mathematical writing avoids this form when the meaning matters. Use parentheses or a fraction bar. So the best answer is: implicit multiplication can be treated as visually tighter by convention in some settings, but you should not rely on that convention for ambiguous expressions.
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