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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.

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    See also this post, – Robert Israel Mar 08 '21 at 01:41
  • @RobertIsrael, here's another related post: https://matheducators.stackexchange.com/questions/7281/how-to-explain-the-difference-between-the-fraction-a-b-and-the-ratio-a-b 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 $B$". – Joe Jul 02 '21 at 17:39

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