# MAT156 Chapter 5-7

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MAT156 Chapter 5-7

## 1. Chapter 5

### 1.1. Chapter 5.1- Addition/Subtraction Integers

1.1.1.1. A. chip model

1.1.1.2. B. Charge-Field model

1.1.1.3. C. Number Line model

1.1.1.3.1. Always start from 0

1.1.1.4. D. Pattern model

1.1.1.4.1. 4+2 4+1 4+0 4+-1 4+-2

1.1.1.5. E. Absolute Value

1.1.1.5.1. Distance between from 1 to that number

1.1.2. Properties

1.1.2.1. Closure

1.1.2.2. Commutatuive

1.1.2.3. Associative

1.1.2.4. Identity

1.1.2.4.1. a+0=a

1.1.2.5. Uniqueness of additive inverse

1.1.2.5.1. a+-a=0

1.1.3. Integer subtraction

1.1.3.1. A. chip model

1.1.3.2. B. Charge-Field model

1.1.3.3. C. Number Line model

1.1.3.3.1. ex) turn around and walk

1.1.3.4. D. Pattern model

1.1.3.4.1. 3-2 3-1 3-0 3--1 3--2

1.1.3.5. E. Sub. using missing addend approach

1.1.3.6. F. Sub. using adding the opposite approach

1.1.3.6.1. keep change change

1.1.3.7. G. Properties of sub.

### 1.2. Chapter 5.2- Mult/Division Integers

1.2.1. Mutlplication of integer

1.2.1.1. A. Pattern model for mult.

1.2.1.1.1. 3 of (-2) -2+-2+-2

1.2.1.2. B. Chip model and charged-field model

1.2.1.3. C. Number Line model

1.2.1.4. D. Properties

1.2.1.5. E. Additive Inverse

1.2.1.5.1. (-2)3=-(2x3) for all integer a (-1)a=-a

1.2.1.5.2. (-a)b=-(ab) (-a)(-b)=(ab)

1.2.1.5.3. a(b-c)=ab-ac

1.2.2. Division of integer

1.2.2.1. 5/12 not work not integer

1.2.3. Order of operation

1.2.3.1. parenthesis Exponents Mult/Division Add/sub

### 1.3. Chapter 5.3- Divisibility

1.3.1. bㅣa

1.3.1.1. b=factor/divisor

1.3.1.2. a= multiple of b

1.3.1.3. b divide a

1.3.2. Rule

1.3.2.1. 2- last digit even

1.3.2.1.1. 632

1.3.2.2. 3 - sum of its digits divisible by 3

1.3.2.2.1. 123

1.3.2.3. 4 - last 2 digits divisible by 4

1.3.2.3.1. 3924

1.3.2.4. 5 - last digit 5/0

1.3.2.4.1. 9995

1.3.2.5. 6 - divisible by 2,3

1.3.2.5.1. 1230

1.3.2.6. 8 - last 3 digits divisible by 8

1.3.2.6.1. 2640

1.3.2.7. 9 - sum of digits dibisible by 9

1.3.2.7.1. 999

1.3.2.8. 10 - last digit 0

1.3.2.8.1. 49940

1.3.2.9. 11 - odd digit- even digit divisible by 11

1.3.2.9.1. 112211

### 1.4. Chapter 5.4- Prime/Composite Numbers

1.4.1. Prime Factorization

1.4.1.1. prime factorization

1.4.1.1.1. only one prime number

1.4.1.2. factor tree

1.4.1.2.1. 24 4 6 22 23

1.4.1.3.1. 2 12 2 6 3 3 1

1.4.1.4. number of division

1.4.1.4.1. 1,2,3,4,6,8,12,24

1.4.1.5. sieve of eratosthenes

### 1.5. Chapter 5.5- GCF/LCM

1.5.1. Greatest Common Factor

1.5.1.1. Colored Rods Meathod

1.5.1.2. intersection of set

1.5.1.2.1. 20-1,2,4,5,10,20 32-1,2,4,8,16,32

1.5.1.3. prime factorization

1.5.1.3.1. 180=2^2x3^2x5 168=2^3x3x7

1.5.1.4. calculator

1.5.1.5.1. 5 25 30 5 6

1.5.2. Least Common Multiple

1.5.2.1. number line

1.5.2.2. Colored Rods Meathod

1.5.2.3. intersection of set

1.5.2.3.1. 2-2,4,6,8,10 3-3,6,9,12,15

1.5.2.4. prime factorization

## 2. Chapter 6.1- Rational Numbers

### 2.1. Rational Number a/b

2.1.1. a= numerator

2.1.2. b= denominator

2.1.3. a divided by b

### 2.2. Use of Rational Numbers

2.2.1. 1. division problem/solution

2.2.1.1. 2x=3; x=3/2

2.2.2. 2. Partition, part of whole

2.2.2.1. Joe ate 1/2 of pizza

2.2.3. 3. Ratio

2.2.3.1. girl : boy = 10:12

2.2.4. Probability

2.2.4.1. toss coin probability is 1/2

### 2.3. Modeling

2.3.1. Area

2.3.2. Number line

2.3.2.1. * hard for kids

2.3.3. Set

### 2.4. Proper Fraction

2.4.1. numerator is smaller than the denominator

2.4.1.1. 3/10

### 2.5. Improper Fraction

2.5.1. numerator is greater than the denominator

2.5.1.1. 12/5

### 2.6. Equivalent or Equal Fractuin

2.6.1. need manipulate

2.6.1.1. Fraction Strip

2.6.2. 1/3=2/6=3/9

2.6.3. value of fraction doesn't change

2.6.4. a/b=an/bn if n is nonzero integer

### 2.7. Simplify Fraction

2.7.1. a/b is simplest form if GCD (a,b)=1

2.7.2. 12/42=2/7

### 2.8. Equality of Fraction

2.8.1. Rewrite both fraction with the same denomiator

2.8.2. 2/5,3/4

2.8.2.1. 8/20,15/20

## 3. 6-2 Adding, Subtracting and Est. Fractions & 6-3 Mult. & Divide Fractions

### 3.1. Addition of Rational numbers

3.1.1. Area model

3.1.2. Number-line model

3.1.3. a/c+b/c=(a+b)/c

### 3.2. Mixed Numbers

3.2.1. 4 1/3

3.2.1.1. 4 whole and one third

### 3.3. Addition Property

3.3.1. Additive Inverse Property

3.3.1.1. a/b+(-a/b)=0

3.3.2. Addition Property of Equality

3.3.2.1. a/b=c/d; a/b+e/f=c/d+e/f

### 3.4. Subtraction

3.4.1. a/b-c/d= a/b+(-c/d)

3.4.2. * bring whole numbers over

### 3.5. mult. of rational numbers

3.5.1. a/b x c/d = ac/bd

### 3.6. Mult. Property

3.6.1. multiplicative identity

3.6.1.1. 1(a/b)=a/b

3.6.2. mult. inverse

3.6.2.1. a/b x b/a = 1

3.6.3. distribution

3.6.3.1. a/b(c/d+e/f) = (a/bxc/d)+(a/bxe/f)

3.6.4. mult. Property of Equality

3.6.4.1. a/b=c/d; a/bxe/f=c/dxe/f

3.6.5. Zero

3.6.5.1. a/b x 0 = 0

3.6.6. inequality

3.6.6.1. a/b>c/d; a/b(e/f) > c/d(e/f)

## 4. 7-1 Introduction to Decimals & 7-2 Operations on Decimals

### 4.2. ones. tens hundredths thousandths ten-thousandth hundred-thousandth

4.2.1. 2.5

4.2.1.1. 2 and 5 tens

### 4.3. expanded form

4.3.1. 5.43= 5+4x10^0+3x10^-1

### 4.4. terminating decimals

4.4.1. no prime rather than 2,5

4.4.1.1. 2.5=25/10

4.4.1.1.1. 10-2,5

4.4.1.2. 2/5=0.4

### 4.7. Scientific Notation

4.7.1. 2,9000,000,000=2.9x10^10

## 5. 7-3 Non-terminating Decimals

### 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