1.1 Whole Number Operations See handout See handout OperationWordsAlgebra Additionthe sum ofa + b Subtractionthe difference ofa - b Multiplicationthe product.

1.1 Whole Number 1.1 Whole Number OperationsOperations

• See handoutSee handout

Operation Words Algebra

Addition the sum of a + b

Subtraction the difference of

a - b

Multiplication the product of a x b, a ∙ b

Division the quotient of a ÷ b, a/b

Addition/Subtraction – On Your Addition/Subtraction – On Your OwnOwn

• Find the value of the expression. Find the value of the expression. Use estimation to check your answer.Use estimation to check your answer.

Multiplication – On Your Multiplication – On Your OwnOwn

• Find the value of the expression. Find the value of the expression. Use estimation to check your answer.Use estimation to check your answer.

Division – On Your OwnDivision – On Your Own

• Find the value of the expression. Find the value of the expression. Use estimation to check your answer.Use estimation to check your answer.

Division – On Your OwnDivision – On Your Own

• Find the value of the expression. Find the value of the expression. Use estimation to check your answer.Use estimation to check your answer.

Division – On Your OwnDivision – On Your Own

Find groups means divide!

1.2 Powers and Exponents1.2 Powers and Exponents

Power – On Your OwnPower – On Your Own

• PowerPower: a product of repeated factors: a product of repeated factors

Write the product as a power:Write the product as a power:

Base and Exponent – On Your Base and Exponent – On Your OwnOwn• BaseBase of a power: the repeated factor of a power: the repeated factor

• ExponentExponent of a power: the number of of a power: the number of times the base is used as a factortimes the base is used as a factor

Find the value of the power:Find the value of the power:

Perfect Square – On Your Perfect Square – On Your OwnOwn

• Perfect squarePerfect square: the square of a : the square of a whole numberwhole number

9 = 39 = 322, so 9 is a perfect square., so 9 is a perfect square.

Determine whether the number is a Determine whether the number is a perfect square:perfect square:

1.3 Order of Operations1.3 Order of Operations

• Numerical expressionNumerical expression: an expression that : an expression that contains only numbers and operationscontains only numbers and operations

• EvaluateEvaluate: to find the value: to find the value

• Order of OperationsOrder of Operations::1.1. PParenthesesarentheses

2.2. EExponentsxponents

3.3. MMultiplication and ultiplication and DDivision left to rightivision left to right

4.4. AAddition and ddition and SSubtraction left to rightubtraction left to right

1.3 Notes1.3 Notes

Using Order of Operations to Using Order of Operations to Evaluate a Numerical ExpressionEvaluate a Numerical Expression

1.11.1

1.4 Prime Factorization1.4 Prime Factorization

• Factor treeFactor tree: a diagram that splits : a diagram that splits whole numbers into factor pairs until whole numbers into factor pairs until all factors are primeall factors are prime

Factor tree for 60Factor tree for 60

• Draw a factor tree for 24Draw a factor tree for 24

Factor Pairs - On Your OwnFactor Pairs - On Your Own

• Factor pairFactor pair: a pair of numbers that : a pair of numbers that are factors of a productare factors of a product

Factor pairs for 12:Factor pairs for 12:

1, 12 (1 x 12 = 12)1, 12 (1 x 12 = 12)

2, 6 (2 x 6 = 12)2, 6 (2 x 6 = 12)

3, 4 (3 x 4 = 12)3, 4 (3 x 4 = 12)

List the factor pairs of the number:List the factor pairs of the number:

Prime Factorization - On Your Prime Factorization - On Your OwnOwn

• Prime factorizationPrime factorization: a composite : a composite number written as a product of its number written as a product of its prime factorsprime factors

The prime factorization of 60:The prime factorization of 60:

Write the prime factorization of the Write the prime factorization of the number:number:

Prime Factorization - On Your Prime Factorization - On Your OwnOwnWhat is the greatest perfect square that is a factor What is the greatest perfect square that is a factor of 1575?of 1575?

1.5 Greatest Common 1.5 Greatest Common FactorFactor• Common factorsCommon factors: factors that are shared : factors that are shared

by two or more numbersby two or more numbers

• Greatest common factorGreatest common factor: the greatest of : the greatest of the common factorsthe common factors

Find the GCF of 24 and 40 using common Find the GCF of 24 and 40 using common factors:factors:

Finding GCF Using Prime Finding GCF Using Prime FactorizationFactorizationFind the GCF of 12 and 56 using prime Find the GCF of 12 and 56 using prime factorization:factorization:

The GCF is 4.The GCF is 4.

Using GCF to Find the Using GCF to Find the Greatest Number of Equal-Greatest Number of Equal-sized Groupssized Groups• You have 24 roses and 36 tulips. What is the You have 24 roses and 36 tulips. What is the

greatest number of identical flower arrangements greatest number of identical flower arrangements you can make?you can make?

24 = 2 ∙ 2 ∙ 2 ∙ 324 = 2 ∙ 2 ∙ 2 ∙ 3

36 = 2 ∙ 2 ∙ 3 ∙ 336 = 2 ∙ 2 ∙ 3 ∙ 3

The common factors are 2, 2, and 3.The common factors are 2, 2, and 3.

The greatest number of identical arrangements isThe greatest number of identical arrangements is

2 ∙ 2 ∙ 3 = 12 2 ∙ 2 ∙ 3 = 12

Notes 1.6: Least Common Notes 1.6: Least Common MultipleMultiple• Common multiplesCommon multiples: multiples that are : multiples that are

shared by two or more numbersshared by two or more numbers

List the common multiples of 4 and 6:List the common multiples of 4 and 6:

• Least common multipleLeast common multiple: the least of the : the least of the common multiplescommon multiples

Finding LCM Using Prime Finding LCM Using Prime FactorizationFactorizationFind the LCM of 16 and 20Find the LCM of 16 and 20

Write what they have in common: Write what they have in common: 2 ∙ 22 ∙ 2

Write the remaining prime factors: Write the remaining prime factors: 2 ∙ 2 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5∙ 2 ∙ 2 ∙ 5

Multiply: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 = 80Multiply: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 = 80

80 is the LCM of 16 and 20.80 is the LCM of 16 and 20.

Finding the LCM of Three Finding the LCM of Three NumbersNumbers

Find the LCM of 4, 15, and 18:Find the LCM of 4, 15, and 18:Write what two or three of the trees have in Write what two or three of the trees have in common: common: 2 ∙ 32 ∙ 3

Write the remaining prime factors: Write the remaining prime factors: 2 ∙ 3 2 ∙ 3 ∙ 2 ∙ 2 ∙ 3 ∙ 5∙ 3 ∙ 5

Multiply. 2 ∙ 3 ∙ 2 ∙ 3 ∙ 5 = 180Multiply. 2 ∙ 3 ∙ 2 ∙ 3 ∙ 5 = 180

180 is the LCM of 4, 15, and 18.180 is the LCM of 4, 15, and 18.

Using LCM to Find When Using LCM to Find When Two Things Happen at Same Two Things Happen at Same TimeTime

On Your OwnOn Your Own

• A traffic light changes every 30 seconds. A traffic light changes every 30 seconds. Another changes every 45 seconds. Both Another changes every 45 seconds. Both lights change. After how many seconds will lights change. After how many seconds will both change at the same time?both change at the same time?

Find LCM of 30 and 45 by listing multiples:Find LCM of 30 and 45 by listing multiples:

30, 60, 90, …30, 60, 90, …

45, 90, …45, 90, …

The lights will change at the same time in 90 seconds The lights will change at the same time in 90 seconds (or one and a half minutes).(or one and a half minutes).

Finding GCF and LCM using Finding GCF and LCM using Inverted DivisionInverted Division

Notes 1.6 Extension: Notes 1.6 Extension: Adding and Subtracting Adding and Subtracting FractionsFractions• Least common denominator: the Least common denominator: the

LCM of the denominatorsLCM of the denominators

• To add and subtract fractions with To add and subtract fractions with unlike denominators:unlike denominators:– Use a common denominator, simplify at Use a common denominator, simplify at

endend– Use the least common denominatorUse the least common denominator