Update Unit 1: Essential Skills.md

Grade 9/Math/MPM1DZ/Unit 1: Essential Skills.md

@@ -5,21 +5,21 @@
 ### Addition / Subtraction
  | Expression | Equivalent|
  |:----------:|:---------:|
- | a + b | a + b |
- | (-a) + b | b - a |
- | a + (-b) | a - b |
- | (-a) + (-b) | -(a + b) |
- | a - b | a - b|
- | a - (-b) | a + b |
- | (-a) -(-b) | (-a) + b|
+ | $`a + b`$ | $`a + b`$ |
+ | $`(-a) + b`$ | $`b - a`$ |
+ | $`a + (-b)`$ | $`a - b`$ |
+ | $`(-a) + (-b)`$ | $`-(a + b)`$ |
+ | $`a - b`$ | $`a - b`$|
+ | $`a - (-b)`$ | $`a + b`$ |
+ | $`(-a) -(-b)`$ | $`(-a) + b`$|
 
 ### Multiplication / Division    
  | Signs | Outcome |
  |:-----:|:-------:|
- | a * b | Positive |
- | (-a) * b | Negative |
- | a * (-b) | Negative |
- | (-a) * (-b) | Positive |
+ | $`a \times b`$ | Positive |
+ | $`(-a) \times b`$ | Negative |
+ | $`a \times (-b)`$ | Negative |
+ | $`(-a) \times (-b)`$ | Positive |
 
 ### BEDMAS / PEMDAS
 -  Follow ```BEDMAS``` for order of operations if there are more than one operation   
@@ -37,7 +37,7 @@
 
 ## Interval Notation
 - A notation that represents an interval as a pair of numbers.     
-- The numbers in the interval represent the endpoint. E.g. **[x > 3, x ∈ R]**   
+- The numbers in the interval represent the endpoint. E.g. $`[x > 3, x \isin R]`$   
 - ```|``` means ```such that```   
 - ```E``` or ∈ means ```element of```      
 - ```N``` represents **Natural Numbers** $`N = \{x | x \gt 0, x \isin \mathbb{Z} \}`$    
@@ -47,10 +47,10 @@
 
   | Symbol | Meaning |
   |:------:|:-------:|
-  | (a, b) | Between but not including ```a``` or ```b```, you also use this for ```∞``` |
-  | [a, b] | Inclusive |
-  | a ∪ b | Union (or) |
-  | a ∩ b | Intersection (and) |
+  | $`(a, b)`$ | Between but not including $`a`$ or $`b`$, you also use this for $`\infty`$|
+  | $`[a, b]`$ | Inclusive |
+  | $`a ∪ b`$ | Union (or) |
+  | $`a ∩ b`$ | Intersection (and) |
 
 ## Pythgorean Theorem
 - a and b are the two legs of the triangle or two sides that form a 90 degree angle of the triangle, c is the hypotenuse        
@@ -71,32 +71,32 @@
 
 ### Example Simplify Fully:
 
-- $` \frac{3}{4} \div \frac{2}{14} `$ Reduce to lowest terms
+- $` \dfrac{3}{4} \div \dfrac{2}{14} `$ Reduce to lowest terms
 
-- $` \frac{3}{4} \div \frac{1}{7} `$ Multiple by reciprocal
+- $` \dfrac{3}{4} \div \dfrac{1}{7} `$ Multiple by reciprocal
 
-- $` \frac{3}{4} \times 7 `$
+- $` \dfrac{3}{4} \times 7 `$
 
-- $` = \frac{21}{4}`$ Leave as improper fraction
+- $` = \dfrac{21}{4}`$ Leave as improper fraction
 
 
 ### Shortcut for multiplying fractions
 - cross divide to keep your numbers small    
 - Example:    
-- $` \frac{3}{4} \times \frac{2}{12} `$
+- $` \dfrac{3}{4} \times \dfrac{2}{12} `$
  
-- $` \frac{1}{2} \times \frac{1}{4} `$
+- $` \dfrac{1}{2} \times \dfrac{1}{4} `$
  
-- $` = \frac{1}{8} `$
+- $` = \dfrac{1}{8} `$
 
 
 ## Exponent Laws
 
  | Rule | Description| Example |
  |:----:|:----------:|:-------:|
- |Product|a<sup>m</sup> &times; a<sup>n</sup> = a<sup>n+m</sup>|2<sup>3</sup> &times; 2<sup>2</sup> = 2<sup>5</sup>|
- |Quotient|a<sup>m</sup> &divide; a<sup>n</sup> = a<sup>n-m</sup>|3<sup>4</sup> &divide; 3<sup>2</sup> = 3<sup>2</sup>|
- |Power of a Power|(a<sup>m</sup>)<sup>n</sup> = a<sup>mn</sup>|(2<sup>3</sup>)<sup>2</sup> = 2<sup>6</sup>|
+ |Product|$`a^m \times a^n = a^{n+m}`$|$`2^3 \times 2^2 = 2^5`$|
+ |Quotient|$`a^m \divide a^n = a^{n-m}`$|$`3^4 \divide 3^2 = 3^2`$|
+ |Power of a Power|$`(a^m)^n = a^mn`$|$`(2^3)^2 = 2^6`$|
  |Power of a Quotient|<img src="http://latex2png.com/output//latex_9528cf1be9ea781a9134559f27f6b94b.png" width="25"> =   <img src="http://latex2png.com/output//latex_8c4a93634d0e2f5cfce05b474ebf2f02.png" width="15">|<img src="http://latex2png.com/output//latex_74d1af968da0b70a335c8d93273635e9.png" width="25"> =   <img src="http://latex2png.com/output//latex_2040cef99eca664c295bd74848f0779f.png" width="15">|
  |Zero as Exponents|a<sup>0</sup> = 1|21<sup>0</sup> = 1|
  |Negative Exponents|a<sup>-m</sup> = <img src="http://latex2png.com/output//latex_0223494d8dd45b887178dcecbbfeb462.png" width="20">|1<sup>-10</sup> = <img src="http://latex2png.com/output//latex_4765f9318cc4813f30321334b18635eb.png" width="20">|