diff --git a/Grade 9/Math.md b/Grade 9/Math.md index e43cd6d..78271d0 100644 --- a/Grade 9/Math.md +++ b/Grade 9/Math.md @@ -42,7 +42,7 @@ >> ```E``` or ∈ means ```element of``` >> ```W``` represents **Whole Numbers** (W = {x | x > 0, x ∈ Z}) >> ```N``` represents **Natural Numbers** (N = {x | x ≥ 0, x ∈ Z}) ->> ```Z``` represents **Integers** (Z = {x | -∞ ≤ x ≥ ∞, x ∈ Z}) +>> ```Z``` represents **Integers** (Z = {x | -∞ ≤ x ≤ ∞, x ∈ Z}) >> ```Q``` represents **Rational Numbers (Q = {ab |a, b ∈ Z, b ≠ 0}) >> | Symbol | Meaning | @@ -59,7 +59,8 @@ >> > ## Operations with Rationals ->> Q = { ab | a, b ∈ Z, b ≠ 0 } +>> Q = { | a, b ∈ Z, b ≠ 0 } +>> >> Any operations with rationals, there are 2 sets of rules >>> 1. ```Rules for operations with integers``` >>> 2. ```Rules for operations with fractions``` @@ -68,17 +69,20 @@ >> 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: ->>> = [Reduce to lowest terms] ->>> = [Multiply by reciprocal] ->>> = × 7 ->>> = [Leave as an improper fraction] +>>> [Reduce to lowest terms] + +>>> [Multiply by reciprocal] + +>>> + +>>> [Leave as an improper fraction] >> ### Shortcut for multiplying fractions >>> cross divide to keep your numbers small ->>> Example: ->>> 24 × 46 ->>> 11 × 13 ->>> = 13 +>>> Example: +>>> +>>> +>>> >> ## Exponent Laws @@ -87,10 +91,10 @@ >>> |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|(ab)n = anbn|(23)4 = 24⁄(34)| +>>> |Power of a Quotient| = | = | >>> |Zero as Exponents|a0 = 1|210 = 1| ->>> |Negative Exponents|a-m = 1am|1-10 = 1⁄(110) or 11| ->>> |Rational Exponents|an/m = (m√a)n|165/4 = (4√16)5 = 25| +>>> |Negative Exponents|a-m = |1-10 = | +>>> |Rational Exponents|an/m = | = | >>> **Note:** >>> Exponential Form --> Expanded Form