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Pre-Algebra > Chapter 2.1 - 2.5 > Flashcards

Chapter 2.1 - 2.5 Flashcards

Evaluate/Simplify/Solve add+subtract Equations/Factors/Factorization/LCM

1
Q

Coefficient

A

the numerical constant that multiplies any variables in an algebraic term

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2
Q

Composite Number

A

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

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3
Q

Division of m by n

A

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”.

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4
Q

Equation

A

Defined as two Expressions connected by an EQUALS SIGN.

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5
Q

What are you doing when you EVALUATE an Algebraic Expression?

A

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

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6
Q

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

A

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.

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7
Q

Define LEAST COMMON MULTIPLE (LCM) of two numbers

A

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

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8
Q

Define the algebraic phrase “LIKE TERMS”

A

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

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9
Q

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

A

You multiply “N” by a Counting Number.

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10
Q

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

A

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

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11
Q

Define PRIME NUMBER

A

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

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12
Q

What does it mean to “SOLVE AN EQUATION”?

A

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

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13
Q

Describe what an algebraic TERM is

A

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

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14
Q

Describe the Notation and Result from the Operation of ADDITION

A

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

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15
Q

Describe the Notation and Result from the Operation of MULTIPLICATION

A

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

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16
Q

Describe the Notation and Result from the Operation of SUBTRACTION

A

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

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17
Q

Describe the Notation and Result from the Operation of DIVISION

A

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

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18
Q

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

A

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

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19
Q

What does a^n mean in Exponential Notation

A

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

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20
Q

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

A

“a” is the BASE; “n” is the EXPONENT

21
Q

How is “a^n” read?

A

“a” to the nth power

22
Q

What is the memonic for Alegbraic Order of Operations?

A

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

23
Q

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

A

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

24
Q

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

A

Exponents: Simplify all expressions with exponents.

25
Q

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

A

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

26
Q

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

A

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

27
Q

What does “Nate’s” stand for in Alegbra memonic Order of Operations?

A

Neighbor Sign Rule: Perform all NEIGHBOR SIGN RULE procedures

28
Q

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

A

Grouping for addition and subrtaction

29
Q

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

A

Same Sign Rule: Perform all SAME SIGN RULE procedures

30
Q

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

A

Mixed Sign Rule: Perform all Mixed Sign Rule procedures

31
Q

Describe how to “Combine Like Terms”

A

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.

32
Q

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

A

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.

33
Q

State the Subtraction Property of Equality

A

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

34
Q

Solve an equation using the Subtraction Property of Equality

A

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.

35
Q

Addition Property of Equality

A

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

36
Q

Solve an equation using Addition Property of Equality

A

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.

37
Q

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

A

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

38
Q

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

A

The SUM of the DIGITS is DIVISIBLE BY 3

39
Q

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

A

The LAST TWO DIGITS are a number DIVISIBLE BY 4

40
Q

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

A

The LAST DIGIT is 5 OR 0

41
Q

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

A

The Number is DIVISIBLE BY BOTH 2 AND 3

42
Q

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

A

The LAST DIGIT is 0

43
Q

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

A

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

44
Q

How to Find ALL the FACTORS of a counting number…

A

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.

45
Q

How to Determine if a number is PRIME…

A

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.

46
Q

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

A

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.

47
Q

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

A

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.

48
Q

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

A

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).

Pre-Algebra (9 decks)

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