Last Sync: 2022-04-29 08:30:46

Mathematics/Prealgebra/Mixed and improper fractions.md

@@ -28,3 +28,21 @@ With the example $4 \frac{7}{8}$, we know this means $4 + \frac{7}{8}$. We need
 $$
     \frac{8}{8} + \frac{8}{8} + \frac{8}{8} + \frac{8}{8} + \frac{7}{8}
 $$
+
+But we know that when we [add fractions with a common denominator](./Add_Subtract_Fractions.md#adding-subracting-fractions-with-common-denominators), we only add the numerators, not the denominators. Thus the calculation would actually be:
+
+$$
+\frac{8 + 8 + 8 + 8 + 7}{8} = \frac{39}{8}
+$$
+
+Addition helps to explain the concepts underlying the procedure but it is more efficient to use multiplication.
+
+The procedure is as follows:
+1. Multiply the whole number part by the denominator
+2. Add the numerator
+3. Place the result over the denominator
+
+Thus:
+$$
+    4 \frac{7}{8} = \frac{(4 \cdot 8) + 7 }{8}
+$$

Programming_Languages/NodeJS/Environments.md

@@ -0,0 +1,6 @@
+---
+tags:
+  - Programming_Languages
+  - backend
+  - node-js
+---

Programming_Languages/NodeJS/Middleware.md

@@ -6,6 +6,7 @@ tags:
   - middleware
 ---
 
+# Middleware 
 ## What is middleware?
 
 * Anything that terminates the `req, res` cycle counts as middleware. It is basically anything that acts as an intermediary once the request is received but before the resource is sent. A good example would be the `app.use(express.json()` or `app.use(bodyParser.json)` functions we call in order to be able to parse JSON that is sent from the client. 
@@ -120,7 +121,7 @@ console.log(app.get("env")); // development
 We can set Morgan to run only in development with:
 
 ```js
-if (app.get("env")) {
+if (app.get("env") === 'development') {
   app.use(morgan("common"));
   console.log('Morgan enabled')
 }