From 05cc520e467823b74b38628288511914a3d906bf Mon Sep 17 00:00:00 2001 From: thomasabishop Date: Fri, 29 Apr 2022 08:30:46 +0100 Subject: [PATCH] Last Sync: 2022-04-29 08:30:46 --- .../Mixed and improper fractions.md | 18 ++++++++++++++++++ Programming_Languages/NodeJS/Environments.md | 6 ++++++ .../NodeJS/{Middlewear.md => Middleware.md} | 3 ++- pdf/Algorithmic_complexity.pdf | Bin 549311 -> 549310 bytes pdf/Arrays.pdf | Bin 83599 -> 83599 bytes pdf/Assembly_programs.pdf | Bin 58049 -> 58049 bytes pdf/Atomic_and_molecular_sentences.pdf | Bin 97737 -> 97737 bytes pdf/Axioms_of_set_theory.pdf | Bin 66749 -> 66749 bytes pdf/Basic_database_concepts.pdf | Bin 99218 -> 99218 bytes pdf/Basic_properties_of_sets.pdf | Bin 128524 -> 128524 bytes pdf/Biconditional_Elimination.pdf | Bin 39042 -> 39042 bytes pdf/Biconditional_Introduction.pdf | Bin 35537 -> 35537 bytes pdf/Binary_arithmetic.pdf | Bin 149838 -> 149838 bytes pdf/Binary_arithmetic_with_circuits.pdf | Bin 357156 -> 357156 bytes pdf/Bits,_bytes,_nibbles.pdf | Bin 51186 -> 51186 bytes pdf/Compile_from_source.pdf | Bin 49795 -> 49795 bytes pdf/Conditional_Elimination.pdf | Bin 43232 -> 43232 bytes pdf/Conditional_Introduction.pdf | Bin 74250 -> 74250 bytes pdf/Conjunction_Elimination.pdf | Bin 47565 -> 47565 bytes pdf/Conjunction_Introduction.pdf | Bin 45840 -> 45840 bytes pdf/Defining_a_computer.pdf | Bin 731550 -> 731550 bytes pdf/Design_features_of_language.pdf | Bin 60132 -> 60132 bytes pdf/Disjunction_Elimination.pdf | Bin 91007 -> 91007 bytes pdf/Disjunction_Introduction.pdf | Bin 54596 -> 54596 bytes pdf/HTTP_request_types.pdf | Bin 46765 -> 46765 bytes pdf/Indeterminacy.pdf | Bin 112534 -> 112534 bytes pdf/Law_of_the_Excluded_Middle.pdf | Bin 35622 -> 35622 bytes pdf/Logic_circuits.pdf | Bin 157687 -> 157687 bytes pdf/Logic_gates.pdf | Bin 407144 -> 407144 bytes pdf/Logical_possibility_and_necessity.pdf | Bin 122811 -> 122811 bytes pdf/Lovelace_quote.pdf | Bin 31770 -> 31770 bytes pdf/Morphology.pdf | Bin 77311 -> 77311 bytes pdf/Negation_Elimination.pdf | Bin 44476 -> 44476 bytes pdf/Negation_Introduction.pdf | Bin 44871 -> 44871 bytes pdf/Object_language_and_meta-language.pdf | Bin 131464 -> 131464 bytes pdf/Package_management_in_Arch.pdf | Bin 71061 -> 71061 bytes pdf/Primary_key.pdf | Bin 80548 -> 80548 bytes pdf/Queue.pdf | Bin 154497 -> 154496 bytes pdf/RESTful_APIs.pdf | Bin 105744 -> 105744 bytes pdf/Recursion.pdf | Bin 176160 -> 176160 bytes pdf/Reiteration.pdf | Bin 53262 -> 53262 bytes pdf/SQL_syntax.pdf | Bin 559941 -> 559941 bytes pdf/Semantic_versioning.pdf | Bin 118251 -> 118251 bytes pdf/Soundness.pdf | Bin 98882 -> 98882 bytes pdf/Stacks.pdf | Bin 151942 -> 151942 bytes pdf/Syllogism.pdf | Bin 79914 -> 79914 bytes pdf/The_Pragmatic_Programmer_1999.pdf | Bin 169339 -> 169339 bytes pdf/The_binary_number_system.pdf | Bin 146858 -> 146858 bytes pdf/Theorems_and_empty_sets.pdf | Bin 75643 -> 75643 bytes pdf/Turing_machines.pdf | Bin 102880 -> 102880 bytes pdf/User_management.pdf | Bin 74126 -> 74126 bytes pdf/Von_Neumann_architecture.pdf | Bin 239665 -> 239665 bytes pdf/Why_computers_use_binary.pdf | Bin 144674 -> 144674 bytes 53 files changed, 26 insertions(+), 1 deletion(-) create mode 100644 Programming_Languages/NodeJS/Environments.md rename Programming_Languages/NodeJS/{Middlewear.md => Middleware.md} (98%) 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. 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