1. Chapter 6.1- Rational Numbers
1.1. Rational Number a/b
1.1.1. a= numerator
1.1.2. b= denominator
1.1.3. a divided by b
1.2. Use of Rational Numbers
1.2.1. 1. division problem/solution
1.2.1.1. 2x=3; x=3/2
1.2.2. 2. Partition, part of whole
1.2.2.1. Joe ate 1/2 of pizza
1.2.3. 3. Ratio
1.2.3.1. girl : boy = 10:12
1.2.4. Probability
1.2.4.1. toss coin probability is 1/2
1.3. Modeling
1.3.1. Area
1.3.2. Number line
1.3.2.1. * hard for kids
1.3.3. Set
1.4. Proper Fraction
1.4.1. numerator is smaller than the denominator
1.4.1.1. 3/10
1.5. Improper Fraction
1.5.1. numerator is greater than the denominator
1.5.1.1. 12/5
1.6. Equivalent or Equal Fractuin
1.6.1. need manipulate
1.6.1.1. Fraction Strip
1.6.2. 1/3=2/6=3/9
1.6.3. value of fraction doesn't change
1.6.4. a/b=an/bn if n is nonzero integer
1.7. Simplify Fraction
1.7.1. a/b is simplest form if GCD (a,b)=1
1.7.2. 12/42=2/7
1.8. Equality of Fraction
1.8.1. Rewrite both fraction with the same denomiator
1.8.2. 2/5,3/4
1.8.2.1. 8/20,15/20
2. 6-2 Adding, Subtracting and Est. Fractions & 6-3 Mult. & Divide Fractions
2.1. Addition of Rational numbers
2.1.1. Area model
2.1.2. Number-line model
2.1.3. a/c+b/c=(a+b)/c
2.1.4. a/b+c/d=(ad+cb)/bd
2.2. Mixed Numbers
2.2.1. 4 1/3
2.2.1.1. 4 whole and one third
2.3. Addition Property
2.3.1. Additive Inverse Property
2.3.1.1. a/b+(-a/b)=0
2.3.2. Addition Property of Equality
2.3.2.1. a/b=c/d; a/b+e/f=c/d+e/f
2.4. Subtraction
2.4.1. a/b-c/d= a/b+(-c/d)
2.4.2. * bring whole numbers over
2.5. mult. of rational numbers
2.5.1. a/b x c/d = ac/bd
2.6. Mult. Property
2.6.1. multiplicative identity
2.6.1.1. 1(a/b)=a/b
2.6.2. mult. inverse
2.6.2.1. a/b x b/a = 1
2.6.3. distribution
2.6.3.1. a/b(c/d+e/f) = (a/bxc/d)+(a/bxe/f)
2.6.4. mult. Property of Equality
2.6.4.1. a/b=c/d; a/bxe/f=c/dxe/f
2.6.5. Zero
2.6.5.1. a/b x 0 = 0
2.6.6. inequality
2.6.6.1. a/b>c/d; a/b(e/f) > c/d(e/f)
3. 7-1 Introduction to Decimals & 7-2 Operations on Decimals
3.1. decimals are most familiar with money
3.2. ones. tens hundredths thousandths ten-thousandth hundred-thousandth
3.2.1. 2.5
3.2.1.1. 2 and 5 tens
3.3. expanded form
3.3.1. 5.43= 5+4x10^0+3x10^-1
3.4. terminating decimals
3.4.1. no prime rather than 2,5
3.4.1.1. 2.5=25/10
3.4.1.1.1. 10-2,5
3.4.1.2. 2/5=0.4
3.5. Algorithm for addition and subtraction
3.6. Algorithm for multiplication and division
3.7. Scientific Notation
3.7.1. 2,9000,000,000=2.9x10^10
4. Chapter 5
4.1. Chapter 5.1- Addition/Subtraction Integers
4.1.1. integer addition
4.1.1.1. A. chip model
4.1.1.2. B. Charge-Field model
4.1.1.3. C. Number Line model
4.1.1.3.1. Always start from 0
4.1.1.4. D. Pattern model
4.1.1.4.1. 4+2 4+1 4+0 4+-1 4+-2
4.1.1.5. E. Absolute Value
4.1.1.5.1. Distance between from 1 to that number
4.1.2. Properties
4.1.2.1. Closure
4.1.2.2. Commutatuive
4.1.2.3. Associative
4.1.2.4. Identity
4.1.2.4.1. a+0=a
4.1.2.5. Uniqueness of additive inverse
4.1.2.5.1. a+-a=0
4.1.3. Integer subtraction
4.1.3.1. A. chip model
4.1.3.2. B. Charge-Field model
4.1.3.3. C. Number Line model
4.1.3.3.1. ex) turn around and walk
4.1.3.4. D. Pattern model
4.1.3.4.1. 3-2 3-1 3-0 3--1 3--2
4.1.3.5. E. Sub. using missing addend approach
4.1.3.6. F. Sub. using adding the opposite approach
4.1.3.6.1. keep change change
4.1.3.7. G. Properties of sub.
4.2. Chapter 5.2- Mult/Division Integers
4.2.1. Mutlplication of integer
4.2.1.1. A. Pattern model for mult.
4.2.1.1.1. 3 of (-2) -2+-2+-2
4.2.1.2. B. Chip model and charged-field model
4.2.1.3. C. Number Line model
4.2.1.4. D. Properties
4.2.1.5. E. Additive Inverse
4.2.1.5.1. (-2)3=-(2x3) for all integer a (-1)a=-a
4.2.1.5.2. (-a)b=-(ab) (-a)(-b)=(ab)
4.2.1.5.3. a(b-c)=ab-ac
4.2.2. Division of integer
4.2.2.1. 5/12 not work not integer
4.2.3. Order of operation
4.2.3.1. parenthesis Exponents Mult/Division Add/sub
4.3. Chapter 5.3- Divisibility
4.3.1. bㅣa
4.3.1.1. b=factor/divisor
4.3.1.2. a= multiple of b
4.3.1.3. b divide a
4.3.2. Rule
4.3.2.1. 2- last digit even
4.3.2.1.1. 632
4.3.2.2. 3 - sum of its digits divisible by 3
4.3.2.2.1. 123
4.3.2.3. 4 - last 2 digits divisible by 4
4.3.2.3.1. 3924
4.3.2.4. 5 - last digit 5/0
4.3.2.4.1. 9995
4.3.2.5. 6 - divisible by 2,3
4.3.2.5.1. 1230
4.3.2.6. 8 - last 3 digits divisible by 8
4.3.2.6.1. 2640
4.3.2.7. 9 - sum of digits dibisible by 9
4.3.2.7.1. 999
4.3.2.8. 10 - last digit 0
4.3.2.8.1. 49940
4.3.2.9. 11 - odd digit- even digit divisible by 11
4.3.2.9.1. 112211
4.4. Chapter 5.4- Prime/Composite Numbers
4.4.1. Prime Factorization
4.4.1.1. prime factorization
4.4.1.1.1. only one prime number
4.4.1.2. factor tree
4.4.1.2.1. 24 4 6 22 23
4.4.1.3. ladder model
4.4.1.3.1. 2 12 2 6 3 3 1
4.4.1.4. number of division
4.4.1.4.1. 1,2,3,4,6,8,12,24
4.4.1.5. sieve of eratosthenes
4.5. Chapter 5.5- GCF/LCM
4.5.1. Greatest Common Factor
4.5.1.1. Colored Rods Meathod
4.5.1.2. intersection of set
4.5.1.2.1. 20-1,2,4,5,10,20 32-1,2,4,8,16,32
4.5.1.3. prime factorization
4.5.1.3.1. 180=2^2x3^2x5 168=2^3x3x7
4.5.1.4. calculator
4.5.1.5. Ladder method
4.5.1.5.1. 5 25 30 5 6
4.5.2. Least Common Multiple
4.5.2.1. number line
4.5.2.2. Colored Rods Meathod
4.5.2.3. intersection of set
4.5.2.3.1. 2-2,4,6,8,10 3-3,6,9,12,15
4.5.2.4. prime factorization
4.5.2.5. Ladder method
5. 7-3 Non-terminating Decimals
5.1. 7/8 = 7ㅣ8.000
5.2. Repeating Decimals
5.2.1. 2.11=0.181818
5.2.1.1. __ 0.18
5.3. Ordering
5.3.1. 1.34783478 1.34782178
5.3.2. __ ___ 0.35 > 0.351