diff --git a/Grade 9/Math/MPM1DZ/Unit 1: Essential Skills.md b/Grade 9/Math/MPM1DZ/Unit 1: Essential Skills.md
index deb171e..780d405 100644
--- a/Grade 9/Math/MPM1DZ/Unit 1: Essential Skills.md
+++ b/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|am × an = an+m|23 × 22 = 25|
- |Quotient|am ÷ an = an-m|34 ÷ 32 = 32|
- |Power of a Power|(am)n = amn|(23)2 = 26|
+ |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| = | = |
|Zero as Exponents|a0 = 1|210 = 1|
|Negative Exponents|a-m = |1-10 = |