diff --git a/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md b/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md
index 7df1de7..0e936a1 100644
--- a/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md
+++ b/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md
@@ -68,10 +68,10 @@
- The numbers in the interval represent the endpoint. E.g. **[x > 3, x ∈ R]**
- ```|``` means ```such that```
- ```E``` or ∈ means ```element of```
-- ```N``` represents **Natural Numbers** (N = {x | x > 0, x ∈ Z})
-- ```W``` represents **Whole Numbers** (W = {x | x ≥ 0, x ∈ Z})
-- ```Z``` represents **Integers** (Z = {x | -∞ ≤ x ≤ ∞, x ∈ Z})
-- ```Q``` represents **Rational Numbers** (Q = {a⁄b |a, b ∈ Z, b ≠ 0})
+- ```N``` represents **Natural Numbers** $`N = \{x | x \gt 0, x \isin \mathbb{Z} \}`$
+- ```W``` represents **Whole Numbers** $`W = \{x | x \ge 0, x \isin \mathbb{Z}\}`$
+- ```Z``` represents **Integers** $`Z = \{x| -\infin \le x \le \infin, x \isin \mathbb{Z}\}`$
+- ```Q``` represents **Rational Numbers** $`Q = \{ \frac{a}{b} |a, b \isin \mathbb{Z}, b \neq 0 \}`$
| Symbol | Meaning |
|:------:|:-------:|
@@ -82,12 +82,12 @@
## 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
-- a2 + b2 = c2
+- $`a^2+b^2=c^2`$
- 
## Operations with Rationals
-- Q = { 
| a, b ∈ Z, b ≠ 0 }
+- $`Q = \{ \frac{a}{b} |a, b \isin \mathbb{Z}, b \neq 0 \}`$
- Any operations with rationals, there are 2 sets of rules
1. ```Rules for operations with integers```
@@ -98,20 +98,25 @@
- To Divide rationals, multiply them by the reciprocal
### Example Simplify Fully:
-- 
[Reduce to lowest terms]
-- 
[Multiply by reciprocal]
+- $` \frac{3}{4} \div \frac{2}{14} `$ Reduce to lowest terms
-- 
+- $` \frac{3}{4} \div \frac{1}{7} `$ Multiple by reciprocal
+
+- $` \frac{3}{4} \times 7 `$
+
+- $` = \frac{21}{4}`$ Leave as improper fraction
-- 
[Leave as an improper fraction]
### Shortcut for multiplying fractions
- cross divide to keep your numbers small
- Example:
-- 
-- 
-- 
+- $` \frac{3}{4} \times \frac{2}{12} `$
+
+- $` \frac{1}{2} \times \frac{1}{4} `$
+
+- $` = \frac{1}{8} `$
+
## Exponent Laws