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Real Numbers Week 1 Topic 1

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**Real Numbers Irrational Numbers Rational Numbers Real Numbers**

Numbers that cannot be written as a fraction √2, π Rational Numbers Numbers that can be written as a fraction Decimals that repeat Decimals that stop √25, ½, 5, 0.123, … Real Numbers Set of all irrational and rational numbers

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**Real Numbers Integers Whole Numbers Natural Numbers**

Positive and negative counting numbers (plus 0) {…-3, -2, -1, 0, 1, 2, 3…) Whole Numbers Counting numbers starting at 0 {0, 1, 2, 3…} Natural Numbers Counting numbers starting at 1 {1, 2, 3…}

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**Real Numbers Infinite sets- not countable Finite sets- countable**

Whole numbers greater than 8 {3, 4, 5 …} Finite sets- countable Integers between 2 and 17 {2, 5, 7, 19, 23}

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**Real Numbers Estimating the value of an irrational number**

Compare perfect square values List perfect squares close to your value √67 √49 = 7; √64 = 8; √81 = 9 67 is between 64 and 81 so √67 is between 8 and 9 8 < √67 < 9

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Real Numbers Which of the following represents an infinite set of numbers? {1/2, 1/3, ¼, 1/5} {Negative integers} {-3, -1, 0, 1, 3} {Natural numbers between 5 and 20}

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Real Numbers Which of the following represents an infinite set of numbers? {1/2, 1/3, ¼, 1/5} This set has a clear start and stop, we see exactly 4 values in the set so it is countable or finite {Negative integers} integers go off to infinite so this set is not countable c. {-3, -1, 0, 1, 3} We can count the 5 values in this set. {Natural numbers between 5 and 20} We can list and count the values in this set. 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

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**Real Numbers Which of the following is an irrational number? a. √5**

7 3.78

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**Real Numbers Which of the following is an irrational number? a. √5**

b. √9 = 3 whole numbers are rational 7 = 7/1 whole numbers are rational 3.78 = 378/100 decimals that stop are rational

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Real Numbers 3. Between which two consecutive integers is √113 ? a. 12 and 13 b. 8 and 9 c. 10 and 11 d. 11 and 12

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Real Numbers 3. Between which two consecutive integers is √113 ? a. 12 and 13 b. 8 and 9 c. 10 and 11 d. 11 and = 64; 92 = 81; 102 = 100; 112 = 121; 122 = 144; 132 = 169

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Number Properties Week 1 topic 2

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Number Properties Number Properties Rap Math Properties

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**Number Properties Commutative Property Associative Property**

Numbers can be added or multiplied in any order. 1 + 2 = 2 + 1 2(3) = 3(2) Associative Property When adding, changing the grouping doesn’t matter. (1 + 2) + 3 = 1 + (2 + 3) When multiplying, changing the grouping doesn’t matter. 2(3x4) = (2x3)4

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**Number Properties Identity Inverse Distributive Property**

Adding 0 doesn’t change a value Multiplying by 1 doesn’t change the value Inverse Adding the opposite gives you 0 Multiplying by the reciprocal gives you 1 Distributive Property 3(a + b) = 3a + 3b

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**Number Properties Closure**

When you add or multiple real numbers together the answer will also be a real number.

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Number Properties

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Number Properties When we multiply by 1 the number keeps its value or “identity”.

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Number Properties

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Number Properties This is the Closure Property

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Number Properties

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Number Properties

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Number Properties

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Number Properties The numbers are being regrouped so this is the associative property.

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Number Properties

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Number Properties The multiplicative inverse is the reciprocal. We use it to make a number turn into 1.

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**Integers and Absolute Values**

Week 1 Topic 3

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**Integers Adding two positive integers Just add.**

Answer will be a positive Adding a positive and a negative Subtract Answer will be the same as the larger of the two numbers Adding two negatives Just add Answer will be negative

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Absolute Value Absolute Value is the distance a number is from zero on the number line. |-2| = 2 |3 – 6| = |-3| = 3

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Order of Operations Week 1 Topic 4

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Order of Operations Order of Operations Rap Order of ops rap 2

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Order of Operations

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**Order of Operations Parenthesis 22 – 2[5 + 3(5)]**

Brackets (more parenthesis) 22 – 2[5 + 15] 22 – 2[20] Multiplication 22 – 40 Subtraction -18

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Order of Operations

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Order of Operations 2[7 + 5(-3)] 2[7 + (-15)] 2(-8) -16

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Order of Operations

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**Order of Operations 2(-48 / 4 x 3) 2(-12 x 3) 2(-36) -72**

This one is tricky…we have to multiply and divide at the same time from left to right.

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Scientific Notation Week 1 Topic 5

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Scientific Notation A number written as a product of a power of 10 and a decimal number greater than or equal to 1 and less than 10. 3.72 x 106 When adding and subtracting the exponents must be the same…or we have to rewrite them in standard form first. 3.72 x x 106 = ( ) x 106 = 5.22 x 106

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**Scientific Notation Multiplying Dividing**

Multiply the factors, add the exponents Dividing Divide the factors, subtract the exponents

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Scientific Notation

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Scientific Notation Since the exponents have the same value we can add the factors 7.8 and -4.2. (We end subtracting) 7.8 – 4.2 = 3.6 So our answer is 3.6 x 1020

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Scientific Notation

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Scientific Notation 5.1 / 1.7 = 3 -6 – (-4) = = -2 3 x 10-2

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Scientific Notation

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**Scientific Notation Asia / Australia (1.72 x 107) / (3.13 x 106)**

1.7 is about half as big as 3.13 1.72/3.13 ≈ .55 Subtract the exponents… 7 – 6 = 1 .55 x 101 = 5.5

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