Chapter 2.1 - 2.5 Flashcards
Evaluate/Simplify/Solve add+subtract Equations/Factors/Factorization/LCM
Coefficient
the numerical constant that multiplies any variables in an algebraic term
Composite Number
a counting number that is factorable (i.e. is not prime).
Division of m by n
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”.
Equation
Defined as two Expressions connected by an EQUALS SIGN.
What are you doing when you EVALUATE an Algebraic Expression?
You are calculating the value of a variable when that variable is replaced by a given number.
Define the term EXPRESSION and describe some forms an Expression may take
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.
Define LEAST COMMON MULTIPLE (LCM) of two numbers
The smallest number that is a multiple of those two numbers.
Define the algebraic phrase “LIKE TERMS”
Algebraic TERMS that are either CONSTANTS, or identical VARIABLES having the same Exponents.
Describe how you get the “Multiple of a number N”
You multiply “N” by a Counting Number.
Describe the process of PRIME FACTORIZATION of a number “N”
You simplify the number “N” down to its PRIME FACTORS, the Product of which always equals the original number “N”.
Define PRIME NUMBER
A counting number that is greater than the counting number “1”, and whose product is always equal to “1” times itself.
What does it mean to “SOLVE AN EQUATION”?
Solving a equation is the process by which the value of the equation’s Variable is determined which makes the equation Algebraically TRUE.
Describe what an algebraic TERM is
A Term is defined as either an equation’s constant, or a constant multiplied by one or more of the equations’s variables.
Describe the Notation and Result from the Operation of ADDITION
Notation is “a+b”, Result is “the SUM of a and b”
Describe the Notation and Result from the Operation of MULTIPLICATION
Notation is “a ⦁ b, (a)(b), (a)b, a(b)”, Result is “the PRODUCT of a and b”
Describe the Notation and Result from the Operation of SUBTRACTION
Notation is “a - b”, Result is “the DIFFERENCE of a and b”
Describe the Notation and Result from the Operation of DIVISION
Notation is “a ÷ b, a/b”, Result is “the QUOTIENT of a and b”
Describe EXPONENTIAL NOTATION in terms of the expression “a^n”
a^n is a factor multiplied by itself n times, if n is a positive integer
What does a^n mean in Exponential Notation
a^n means that we multiply “a” by “n” number of factors of “a”
Looking at “a^n” in terms of Exponential Notation - which is the BASE; which is the EXPONENT?
“a” is the BASE; “n” is the EXPONENT
How is “a^n” read?
“a” to the nth power
What is the memonic for Alegbraic Order of Operations?
“Please Eat More Dessert, Nate’s Great Strawberry Mousse”
What does “P lease” stand for in Alegbra memonic Order of Operations?
Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost paretheses first.
What does “Eat” stand for in Alegbra memonic Order of Operations?
Exponents: Simplify all expressions with exponents.
What does “More” stand for in Alegbra memonic Order of Operations?
Multiplication: Perform all multiplication in order starting from left to right.
What does “Dessert” stand for in Alegbra memonic Order of Operations?
Division: Perform all division in order starting from left to right.
What does “Nate’s” stand for in Alegbra memonic Order of Operations?
Neighbor Sign Rule: Perform all NEIGHBOR SIGN RULE procedures
What does “Great” stand for in Alegbra memonic Order of Operations?
Grouping for addition and subrtaction
What does “Strawberry” stand for in Alegbra memonic Order of Operations?
Same Sign Rule: Perform all SAME SIGN RULE procedures
What does “Mousse” stand for in Alegbra memonic Order of Operations?
Mixed Sign Rule: Perform all Mixed Sign Rule procedures
Describe how to “Combine Like Terms”
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.
How do you determine whether a number is a solution to an equation using the subtraction and addition properties of Equality?
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.
State the Subtraction Property of Equality
FOR ANY NUMBERS a,b, and c: IF a = b, THEN a - c = b - c
Solve an equation using the Subtraction Property of Equality
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.
Addition Property of Equality
FOR ANY NUMBERS a,b, and c: IF a = b, THEN a + c = b + c
Solve an equation using Addition Property of Equality
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.
Find Multiples and Factors - A Number is Divisible by “2”, IF
The LAST DIGIT IS EITHER: 0,2,4,6, OR 8.
Find Multiples and Factors - A Number is Divisible by “3”, IF
The SUM of the DIGITS is DIVISIBLE BY 3
Find Multiples and Factors - A Number is Divisible by “4”, IF
The LAST TWO DIGITS are a number DIVISIBLE BY 4
Find Multiples and Factors - A Number is Divisible by “5”, IF
The LAST DIGIT is 5 OR 0
Find Multiples and Factors - A Number is Divisible by “6”, IF
The Number is DIVISIBLE BY BOTH 2 AND 3
Find Multiples and Factors - A Number is Divisible by “10”, IF
The LAST DIGIT is 0
Rule of FACTORS: IF “a ⦁ b = m”, THEN…
Both “a and b” are FACTORS OF “m”, and “m” is the product of a and b.
How to Find ALL the FACTORS of a counting number…
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.
How to Determine if a number is PRIME…
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.
How to Find the Prime Factorization of a Composite number using the TREE Method
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.
How to Find the Prime Factorization of a Composite number using the LADDER Method.
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.
How to Find the Lowest Common Multiple (LCM) by listing multiples
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).
