diff --git a/Mathematics/Prealgebra/Mixed and improper fractions.md b/Mathematics/Prealgebra/Mixed and improper fractions.md index 8b05480..885d04a 100644 --- a/Mathematics/Prealgebra/Mixed and improper fractions.md +++ b/Mathematics/Prealgebra/Mixed and improper fractions.md @@ -27,4 +27,22 @@ Mixed fractions are hard to calculate with. We need some way to convert them to With the example $4 \frac{7}{8}$, we know this means $4 + \frac{7}{8}$. We need to express the amount 4 in terms of eighths. It would be 4 lots of $\frac{8}{8}$ given that 4 is a whole number not a fractional amount. Thus the process would be: $$ \frac{8}{8} + \frac{8}{8} + \frac{8}{8} + \frac{8}{8} + \frac{7}{8} +$$ + +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: +$$ + 4 \frac{7}{8} = \frac{(4 \cdot 8) + 7 }{8} $$ \ No newline at end of file diff --git a/Programming_Languages/NodeJS/Environments.md b/Programming_Languages/NodeJS/Environments.md new file mode 100644 index 0000000..019dd79 --- /dev/null +++ b/Programming_Languages/NodeJS/Environments.md @@ -0,0 +1,6 @@ +--- +tags: + - Programming_Languages + - backend + - node-js +--- diff --git a/Programming_Languages/NodeJS/Middlewear.md b/Programming_Languages/NodeJS/Middleware.md similarity index 98% rename from Programming_Languages/NodeJS/Middlewear.md rename to Programming_Languages/NodeJS/Middleware.md index b365a02..0333854 100644 --- a/Programming_Languages/NodeJS/Middlewear.md +++ b/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') } diff --git a/pdf/Algorithmic_complexity.pdf b/pdf/Algorithmic_complexity.pdf index cf1aa60..5cd8916 100644 Binary files a/pdf/Algorithmic_complexity.pdf and b/pdf/Algorithmic_complexity.pdf differ diff --git a/pdf/Arrays.pdf b/pdf/Arrays.pdf index 4b480b8..ccf5c3d 100644 Binary files a/pdf/Arrays.pdf and b/pdf/Arrays.pdf differ diff --git a/pdf/Assembly_programs.pdf b/pdf/Assembly_programs.pdf index eea2b06..2486f00 100644 Binary files a/pdf/Assembly_programs.pdf and b/pdf/Assembly_programs.pdf differ diff --git a/pdf/Atomic_and_molecular_sentences.pdf 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