# MAT 156

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MAT 156

## 6. Exam 1

### 6.1. Four-Step Problem Solving

6.1.1. 1.) Understanding the Problem =What is the problem, what info is needed, unknowns?,

6.1.1.1. 2. Devising a Plan= Patterns, table, diagram, write an equation, work backwards, sub goals

6.1.1.1.1. 3. Carrying out the plan = Perform strategies from step 2, check, keep accurate record

### 6.2. Arithmetic Sequence = When the successive term is obtained from the previous term by + or - of a fixed #

6.2.1. Fibonacci = 1st and 2nd term become 3rd, 2nd and 3rd become 4th = Fn=Fn-1+Fn-2

6.2.1.1. Geometric= an=a1xr^n-1 a=first term r=ratio n=desired ratio

6.2.2. Fibonacci = 1st and 2nd # become 3rd, 2nd and 3rd become 4th, ... Fn=Fn-1+Fn-2

6.2.2.1. Geometric = an=a1xr^n-1 a1=1st term r=ratio n=desired ratio

## 7. Exam 2

### 7.3. Closure Property= If a and b are whole numbers then a+b is a whole number

7.3.1. Commutative Property=a+b=b+a

7.3.1.1. Associative Property=(a+b)+c=a+(b+c) also known as grouping property

7.3.1.1.1. Identity Property=a+0=a

### 7.5. Properties of Whole Number Multiplication

7.5.1. Closure= axb=unique whole #

7.5.1.1. Commutative= axb=bxa

7.5.1.1.1. Associative= (axb)xc=ax(bxc)

### 7.6. Set (Partition)Model= 18 cookies divided by 3 would be 3 sets of 6 cookies

7.6.1. Missing-Factor Model 3xc=18 3x6=18 c=6

7.6.1.1. Repeated Subtraction Model= 18-6=12-6=6-6=0

### 7.7. Long Division

7.7.1. Divide, Multiply, Subtract, Check, Bring Down, Circle

### 7.8. Any ordered pair is a relation

7.8.1. A function is one output for each input <=not a function >=function

## 8. Exam 3

8.1.1. Black chips are used to represent positive integers and negative integers ares red

### 8.2. Charge field model

8.2.1. Similar to chips, but use the positive and negative charges

### 8.3. Number line model

8.3.1. Always start at 0 and move line to first number, then go to second number.

### 8.4. Pattern Model

8.4.1. Addition of integers can also be motivated by using patterns of addition of whole numbers

### 8.5. Absolute value

8.5.1. The distance between the point corresponding to an integer and 0 is the absolute value of the integer.

### 8.6. properties of Integer Addition

8.6.1. closure property of addition of intergers

8.6.2. commutative property of addition of integers

8.6.3. associative property of addition of integers

8.6.4. indetify element of addition of integers

### 8.7. divisibility rules

8.7.1. divisibility rules for,

8.7.1.1. 2 and integer is divisible by 2 if it last units digits are divisble by 2

8.7.1.2. 3 an integer is divisble by 3 if the sum of its digits are divisible by 3

8.7.1.3. 4 and integer is divisble by 4 if the last two digits represent a number divisible by 4

8.7.1.4. 5 an integer is divisble by 5 if the last digit is 0 or 5

8.7.1.5. 6 an integer is divisible by 6 if the integer is divisible by 2 and 3

8.7.1.6. 8 an integer is divisible by 8 if the last three digits of the represent and integer divisible by 8

8.7.1.7. 9 an integer is divisble by 9 if the sum of the digits of the integer is divisble by 9

8.7.1.8. 10 an integer is divisble by ten if the last digit is a zero

8.7.1.9. 11 an integer is divisible by 11 if the sum of the digits in the places that are even powers of 10 minus the sum of the digits in the places that are odd powers of 10 is divisible by 11

### 8.8. Numbers

8.8.1. Prime= #'s in which there are only two factors or positive divisors

8.8.2. Composite+ #'s in which there are more than two factors or positive divisors

### 8.9. Properties of Integer Multiplication

8.9.1. 1. Closure property of multiplication of integers- ab is a unique #

8.9.1.1. 2. Commutative property of multiplication of integers- ab=ba

8.9.1.1.1. 3. Associative property of multiplication of integers- (ab)c=a(bc)

8.9.2. Rules for negative and positive multiplication

### 8.11. GCF VS LCM

8.11.1. GCF- The greater common divisor of two natural numbers a and b is the greatest natural number that divides both a and b.

8.11.1.1. LCM- Least Common Multiple- The least common multiple of a and b is the least natural number that is simultaneously a multiple of a and a multiple of b.

## 9. Exam 4

### 9.1. Proper Fraction: a/b where 0 is less than or equal to a, and a is less than b= numerator is smaller than the denominator.

9.1.1. Improper Fraction: a/b where a is greater than or equal to b, and b is greater than 0= numerator is greater than denominator.

### 9.2. Simplifying Fractions

9.2.1. a/b in simplest is form is diving both a and b by the GCF

### 9.3. Equality of Fractions

9.3.1. Rewrite both fractions with LCM

9.3.1.1. EX: 12/42 = 420/1470

### 9.4. Addition of Rational Numbers with Like Denominators

9.4.1. if a/b and c/b are rational #'s, then, a/b+c/b=a+c/b

9.4.1.1. Addition of Rational Numbers with Unlike Denominators

9.4.1.1.1. If a/b and c/b are rational #'s, then, a/b+c/d=ad+cb/bd

### 9.5. Properties of Addition for Rational Numbers

9.5.1. Integers...= 1.) -(-a)=a 2.) -(a+b)=-a+-b

9.5.1.1. Rational Numbers...= 1.) -(-a/b)=a/b 2.)-(a/b+c/d)=-a/b=-c/d

### 9.6. Properties of Multiplication of Rational Numbers

9.6.1. 1x_a/b)=a/b+(a/b)x1

9.6.1.1. Inverse= a/bxb/a=1=b/axa/b

### 9.8. Terminations Decimals= Finite number

9.8.1. Repeating Decimals= the repeating block of digits is the repetend.