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+# Unit 1: Essential Skills
+
+## Simple Arithmetics
+
+### 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|
+
+### Multiplication / Division
+ | Signs | Outcome |
+ |:-----:|:-------:|
+ | a * b | Positive |
+ | (-a) * b | Negative |
+ | a * (-b) | Negative |
+ | (-a) * (-b) | Positive |
+
+### BEDMAS / PEMDAS
+- Follow ```BEDMAS``` for order of operations if there are more than one operation
+
+ | Letter | Meaning |
+ |:------:|:-------:|
+ | B / P | Bracket / Parentheses |
+ | E | Exponent |
+ | D | Divison |
+ | M | Multiplication |
+ | A | Addition |
+ | S | Subtraction |
+
+- 
+
+## 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]**
+- ```|``` means ```such that```
+- ```E``` or ∈ means ```element of```
+- ```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 |
+ |:------:|:-------:|
+ | (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) |
+
+## 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
+- $`a^2+b^2=c^2`$
+
+- 
+
+## Operations with Rationals
+- $`Q = \{ \frac{a}{b} |a, b \isin \mathbb{Z}, b \neq 0 \}`$
+
+- Any operations with rationals, there are 2 sets of rules
+ 1. ```Rules for operations with integers```
+ 2. ```Rules for operations with fractions```
+
+- To Add / subtract rationals, find common denominator and then add / subtract numerator
+- To Multiply rationals, first reduce the fraction to their lowest terms, then multiply numerators and denominators
+- To Divide rationals, multiply them by the reciprocal
+
+### Example Simplify Fully:
+
+- $` \frac{3}{4} \div \frac{2}{14} `$ 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
+
+
+### 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
+
+ | 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|
+ |Power of a Quotient|
= 
|
= 
|
+ |Zero as Exponents|a0 = 1|210 = 1|
+ |Negative Exponents|a-m = 
|1-10 = 
|
+ |Rational Exponents|an/m = 
|
= |
+
+**Note:**
+- Exponential Form --> Expanded Form
+- 64 = 6 × 6 × 6 × 6
+
+## Scientific Notation
+- They convey accuracy and precision. It can either be written as its original number or in scientific notation:
+- 555 (**Exact**) or $`5.55 \times 10^2`$ (**3 significant figures**).
+- In scientific notation, values are written in the form $`a(10^n)`$, where $`a`$ is a number within 1 and 10 and $`n`$ is any integer.
+- Some examples include the following: $`5.4 \times 10^3, 3.0 \times 10^2`$, and $`4.56 \times 10^{-4}`$.
+- When the number is smaller than 1, a negative exponent is used, when the number is bigger than 10, a positve exponent is used
+
+- 
+
+- **Remember**: For scientific notation, round to ```3 significant``` digits
+
+## Rates, Ratio and Percent
+- ```Ratio```: A comparison of quantities with the same unit. These are to be reduced to lowest terms.
+- Examples: ```a:b, a:b:c, a/b, a to b ```
+
+- ```Rates```: A comparison of quantities expressed in different units.
+- Example: ```10km/hour```
+
+- ```Percent```: A fraction or ratio in which the denominator is 100
+- Examples: ```50%, 240/100```
+
+## Number Lines
+- a line that goes from a point to another point, a way to visualize set notations and the like
+- 
+- A solid filled dot is used for ```[]``` and a empty dot is used for ```()```
+
+
+## Tips
+- Watch out for the ```+/-``` signs
+- Make sure to review your knowledge of the exponent laws
+- For scientific notation, watch out for the decimal point
+- Use shortcut when multiplying fractions
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