Chapter 2.1 - 2.5

Question 1

Coefficient

Answer 1

the numerical constant that multiplies any variables in an algebraic term

Question 2

Composite Number

Answer 2

a counting number that is factorable (i.e. is not prime).

Question 3

Division of m by n

Answer 3

If a number “M” is the product of some mulltiple of the number “N”, then the number M is also DIVISIBLE by that same number “N”.

Question 4

Equation

Answer 4

Defined as two Expressions connected by an EQUALS SIGN.

Question 5

What are you doing when you EVALUATE an Algebraic Expression?

Answer 5

You are calculating the value of a variable when that variable is replaced by a given number.

Question 6

Define the term EXPRESSION and describe some forms an Expression may take

Answer 6

An algebraic Expression can take the form of a single Number, a single Variable or a combination of several Numbers and Variables connected by one or more algebraic Operation Symbols.

Question 7

Define LEAST COMMON MULTIPLE (LCM) of two numbers

Answer 7

The smallest number that is a multiple of those two numbers.

Question 8

Define the algebraic phrase “LIKE TERMS”

Answer 8

Algebraic TERMS that are either CONSTANTS, or identical VARIABLES having the same Exponents.

Question 9

Describe how you get the “Multiple of a number N”

Answer 9

You multiply “N” by a Counting Number.

Question 10

Describe the process of PRIME FACTORIZATION of a number “N”

Answer 10

You simplify the number “N” down to its PRIME FACTORS, the Product of which always equals the original number “N”.

Question 11

Define PRIME NUMBER

Answer 11

A counting number that is greater than the counting number “1”, and whose product is always equal to “1” times itself.

Question 12

What does it mean to “SOLVE AN EQUATION”?

Answer 12

Solving a equation is the process by which the value of the equation’s Variable is determined which makes the equation Algebraically TRUE.

Question 13

Describe what an algebraic TERM is

Answer 13

A Term is defined as either an equation’s constant, or a constant multiplied by one or more of the equations’s variables.

Question 14

Describe the Notation and Result from the Operation of ADDITION

Answer 14

Notation is “a+b”, Result is “the SUM of a and b”

Question 15

Describe the Notation and Result from the Operation of MULTIPLICATION

Answer 15

Notation is “a ⦁ b, (a)(b), (a)b, a(b)”, Result is “the PRODUCT of a and b”

Question 16

Describe the Notation and Result from the Operation of SUBTRACTION

Answer 16

Notation is “a - b”, Result is “the DIFFERENCE of a and b”

Question 17

Describe the Notation and Result from the Operation of DIVISION

Answer 17

Notation is “a ÷ b, a/b”, Result is “the QUOTIENT of a and b”

Question 18

Describe EXPONENTIAL NOTATION in terms of the expression “a^n”

Answer 18

a^n is a factor multiplied by itself n times, if n is a positive integer

Question 19

What does a^n mean in Exponential Notation

Answer 19

a^n means that we multiply “a” by “n” number of factors of “a”

Question 20

Looking at “a^n” in terms of Exponential Notation - which is the BASE; which is the EXPONENT?

Answer 20

“a” is the BASE; “n” is the EXPONENT

Question 21

How is “a^n” read?

Answer 21

“a” to the nth power

Question 22

What is the memonic for Alegbraic Order of Operations?

Answer 22

“Please Eat More Dessert, Nate’s Great Strawberry Mousse”

Question 23

What does “P lease” stand for in Alegbra memonic Order of Operations?

Answer 23

Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost paretheses first.

Question 24

What does “Eat” stand for in Alegbra memonic Order of Operations?

Answer 24

Exponents: Simplify all expressions with exponents.

Question 25

What does "More" stand for in Alegbra memonic Order of Operations?

Answer 25

Multiplication: Perform all multiplication in order starting from left to right.

Question 26

What does "Dessert" stand for in Alegbra memonic Order of Operations?

Answer 26

Division: Perform all division in order starting from left to right.

Question 27

What does "Nate's" stand for in Alegbra memonic Order of Operations?

Answer 27

Neighbor Sign Rule: Perform all NEIGHBOR SIGN RULE procedures

Question 28

What does "Great" stand for in Alegbra memonic Order of Operations?

Answer 28

Grouping for addition and subrtaction

Question 29

What does "Strawberry" stand for in Alegbra memonic Order of Operations?

Answer 29

Same Sign Rule: Perform all SAME SIGN RULE procedures

Question 30

What does "Mousse" stand for in Alegbra memonic Order of Operations?

Answer 30

Mixed Sign Rule: Perform all Mixed Sign Rule procedures

Question 31

Describe how to "Combine Like Terms"

Answer 31

Step 1: Identify like terms; Step 2: Rearrange the expressions in such a way as though you've grouped like terms together; Step 3:Add the coefficients of the like terms.

Question 32

How do you determine whether a number is a solution to an equation using the subtraction and addition properties of Equality?

Answer 32

Step 1: Substitute the number for the variable in the equation; Step 2: Simplify the expressions on bothe sides of the equation; Step 3: Determine whether the resultinig equation is truse. If it is true, the number is a solution. If it is not true, the number is not a solution.

Question 33

State the Subtraction Property of Equality

Answer 33

FOR ANY NUMBERS a,b, and c: IF a = b, THEN a - c = b - c

Question 34

Solve an equation using the Subtraction Property of Equality

Answer 34

Step 1: Use the Subtraction Preperty of equality to isolate the variable; Step 2: Simplify the expressions on both sides of the equation; Step 3: Check the solution.

Question 35

Addition Property of Equality

Answer 35

FOR ANY NUMBERS a,b, and c: IF a = b, THEN a + c = b + c

Question 36

Solve an equation using Addition Property of Equality

Answer 36

Step 1: Use the Addition Property of Equality to isolate the variable; Step 2: Simplify the expressions on both sides of the equation; Step 3: Check the solution.

Question 37

Find Multiples and Factors - A Number is Divisible by "2", IF

Answer 37

The LAST DIGIT IS EITHER: 0,2,4,6, OR 8.

Question 38

Find Multiples and Factors - A Number is Divisible by "3", IF

Answer 38

The SUM of the DIGITS is DIVISIBLE BY 3

Question 39

Find Multiples and Factors - A Number is Divisible by "4", IF

Answer 39

The LAST TWO DIGITS are a number DIVISIBLE BY 4

Question 40

Find Multiples and Factors - A Number is Divisible by "5", IF

Answer 40

The LAST DIGIT is 5 OR 0

Question 41

Find Multiples and Factors - A Number is Divisible by "6", IF

Answer 41

The Number is DIVISIBLE BY BOTH 2 AND 3

Question 42

Find Multiples and Factors - A Number is Divisible by "10", IF

Answer 42

The LAST DIGIT is 0

Question 43

Rule of FACTORS: IF "a ⦁ b = m", THEN…

Answer 43

Both "a and b" are FACTORS OF "m", and "m" is the product of a and b.

Question 44

How to Find ALL the FACTORS of a counting number…

Answer 44

Step 1: Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor. A): If the resulting quotient is a COUNTING NUMBER, the divisor and quotient are a pair of factors. B): If the quotient is not a counting number, the divisor is not a factor; Step 2: List all the factor pairs; Step 3: Write all the factors in order from smallest to largest.

Question 45

How to Determine if a number is PRIME…

Answer 45

Step 1: Test each of the primes, in order, to see if it is a factor of the number; Step 2: Start with 2 and stop when the quotient is smaller than the divisor, when a prime factor is found; Step 3: If the number has a prime factor, then it is a COMPOSITE NUMBER. If the number has no prime factors, then the number is PRIME.

Question 46

How to Find the Prime Factorization of a Composite number using the TREE Method

Answer 46

Step 1. Find any factor pair of the given number, and use these numbers to create two branches; Step 2. If a factor is prime, that branch is complete. Circle the prime.; Step 3: If a factor is not prime, write it as the product of a factor pair and continue the process; Step 4: Write the composite number as the product of all the circled primes.

Question 47

How to Find the Prime Factorization of a Composite number using the LADDER Method.

Answer 47

Step 1. Divide the number by the smallest prime; Step 2: Continue dividing by that prime until it no longer divides evenly; Step 3: Divide by the next prime until it no longer divides evenly; Step 4. continue until the quotient is a prime; Step 5: Write the composite number as the product of all the primes on the sides and top of the ladder.

Question 48

How to Find the Lowest Common Multiple (LCM) by listing multiples

Answer 48

Step 1. List the first several multiples of each number; Step 2: Look for multiple common to both lists. If there are no common multiple in the lists, write out additional multiples for each number; Step 3 Look for the smallest number that is common to both lists; Step 4: This number is the Lowest Common Multiple (LCM).