doc: math example

backend/README.md

@@ -56,6 +56,13 @@ src
     - [Decimal.js](https://mikemcl.github.io/decimal.js/) is used for the basic arithmetic operations.
 4. Evaluate the result by `Fraction.evaluate()`.
 
+### Example
+1. Input string: `5 / 3 / 4 * 9 - 2 * 3 / 8`
+2. Parse into sub-expressions: `5 / 3 / 4 * 9` and `-2 * 3 / 8`
+3. Turn these into fractions: $\frac{5*9}{3*4}$ and -$\frac{2*3}{8}$
+4. find equivalent fractions with same denominator: $\frac{90}{24}$ and -$\frac{18}{24}$
+5. Sum these fractions: $\frac{90}{24} - \frac{18}{24} = \frac{72}{24} = 3$
+
 ### Limitations
 - All whitespace is ignored, therefore `1 + 2 3` will consider as `1 + 23`
 - `negative sign` is only allowed at the beginning of an expression but not after multiplication or division