# \times vs. \cdot vs. parentheses vs. nothing while writing fraction multiplications

Is there a convention around writing multiplication of fractions. Let us take two examples to be specific.

### Example A: $$2 \times \frac{1}{2}$$

Here are some ways to write this example:

• $$2 \frac{1}{2}$$ (does not seem like a good idea because this means $$2.5$$)
• $$2 \times \frac{1}{2}$$
• $$2 \cdot \frac{1}{2}$$
• $$(2) \left( \frac{1}{2} \right)$$

### Example B: $$\frac{1}{2} \times \frac{3}{4}$$

Here are some ways to write this example:

• $$\frac{1}{2} \frac{3}{4}$$
• $$\frac{1}{2} \times \frac{3}{4}$$
• $$\frac{1}{2} \cdot \frac{3}{4}$$
• $$\frac{1}{2} \left( \frac{3}{4} \right)$$
• $$\left( \frac{1}{2} \right) \left( \frac{3}{4} \right)$$

Is there a preferred way of writing such multiplications in each case?

• In both cases I would bracket the second term and leave the first. Commented Feb 23, 2019 at 14:48
• I personally prefer "$\cdot$" over all of the others. It makes it clear without of the need of say many redundant parentheses, Commented Feb 23, 2019 at 14:48

It’s purely a matter of personal preference, and perhaps of emphasis in context.

For your cases, I would typically use $$2\left(\tfrac12\right)$$ and $$\tfrac12\left(\tfrac34\right),$$ but you are likely to get other answers from other people.

I prefer to omit the multiplication symbol unless that makes the expression appear ambiguous or confusing.

I point out that you have omitted the “in-line” form $$a/b$$ which will often require parentheses on its own to avoid ambiguity. For example, $$\tfrac{x+1}{x-1}$$ is entirely distinct from $$x+1/x-1$$ and I should have written the latter as $$(x+1)/(x-1)$$ if the former were intended.

• I would certainly never use "$2\frac{1}{2}$" or "$\frac{1}{2}\frac{3}{4}$". I would probably tend to use $\left(\frac{1}{2}\right)\left(\frac{3}{4}\right)$ or $\frac{1}{2}\left(\frac{3}{4}\right)$ Commented Feb 23, 2019 at 14:58
• @user247327 : Agreed on the first point: $2\tfrac12$ already has the meaning $2+\tfrac12$ (a mixed fraction) and juxtaposition in this case NEVER indicates multiplication. But I disagree on the second point: $\tfrac12\tfrac34$ is perfectly acceptable and always indicates a product. There is, however, the danger that it might appear as $\tfrac{13}{24}$ if the fraction bars are not clearly separated.
– MPW
Commented Feb 23, 2019 at 15:06
• What happens if we have more than $2$ fractions e.g. $\frac12\frac89\frac34$? Commented Feb 23, 2019 at 15:37
• I would say that $$1\cdot\frac12+\frac12\cdot\frac13+\frac13\cdot\frac14+\ldots$$ looks imho more aesthetically pleasing than $$1\left(\frac12\right)+\left(\frac12\right)\left(\frac13\right)+\left(\frac13\right)\left(\frac14\right)+\ldots$$
– A.Γ.
Commented Feb 23, 2019 at 15:56
• What's wrong with $$1 \left(\frac{1}{2}\right) + \frac{1}{2} \frac{1}{3} + \frac{1}{3} \frac{1}{4} + ...$$ No multiplication signs needed, still unambiguous.
– Zak
Commented May 23 at 15:37

When you only have one kind of multiplication I recommend making it $$\cdot$$ (or $$\times$$ if aimed at a young audience, those who teach team or normal adults), but even then you only need to show it if there's a risk people won't know multiplication is intended, e.g. in distinguishing $$2+\frac12$$ from $$2\times\frac12$$.

Some kinds of "multiplication" have preferred symbols, such as scalar products on vectors ($$\cdot$$) or the "cross products" on $$3$$- or $$7$$-dimensional vector spaces ($$\times$$). When that happens, I recommend using whichever of these symbols is unused for a second kind of multiplication you need to discuss, or $$\otimes$$ (\otimes) if you need a third; but if you do have multiple operators on the go, make their meaning explicit in the text unless it's very standard, e.g. $$a\cdot b\times c$$ with vectors.

If you have closely related operators, such as the multiplication operations on multiple levels of the Cayley-Dickson construction, you might use subscripts (or hope the reader can disambiguate themselves). For example, the dimension-$$2^n$$ algebra with multiplication operator $$\otimes_n$$ gives way to the next viz. $$(p,\,q)\otimes_{n+1}(r,\,s)=(p\otimes_n r-s^\ast\otimes_n q,\,s\otimes_n p+q\otimes_n r^\ast).$$(To my mind $$\otimes_n$$ works much better for this than $$\cdot_n$$ or $$\times_n$$, contra the above advice for cases without subscripts, partly due to kerning issues.) But personally, I think in that case it looks even better to omit the operators, like so: $$(p,\,q)(r,\,s)=(pr-s^\ast q,\,sp+qr^\ast).$$