# Do "the ratio of A to B" and "A:B" always mean A/B as a fraction?

## Question

• Do the expressions "the ratio of A to B" and "A:B" always mean the same as $$\frac{A}{B}$$ (i.e. A divided by B) and not $$\frac{B}{A}$$?

I found several sources that use "the ratio of A to B" as $$\frac{A}{B}$$ and one source that uses "A:B" as $$\frac{A}{B}$$. These sources listed below.

## Sources that use "the ratio of A to B" as $$\frac{A}{B}$$

The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle. $$csc(A) = \frac{hypotenuse}{opposite}$$

Greek letter π to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in 1706.

The a to b ratio is 1:2.

The ratio of a to b is 0.5

## Sources that use "A:B" as $$\frac{A}{B}$$

The a:b ratio is 0.5.

• @RobertIsrael, here's another related post: matheducators.stackexchange.com/questions/7281/… Is there a consensus on whether there is a widely adopted convention on whether $C=A/B$ can be expressed in English as "$C$ is the ratio of $A$ to $B$"? It doesn't seem as eloquent to write, "$C$ is the result of dividing $A$ by $B$" or "$C$ is the fraction $A$ over $B$".