6th Semester 1 Review

Spiral Review

1

​Place & Value

You are finding where the digit is and answering HOW MUCH it is WORTH.

Value​

You are finding where the digit is and answering WHERE it is based on its location.

Place Value Place

​What is place value?

​The place a digit appears in a number determines it's value.

​

​A digit's place value tells how much the digit is worth within the entire number.

Match

Match the following

• $$\frac{1}{10}$$  

• $$\frac{1}{100}$$  

• $$\frac{1}{1000}$$  

0.1

0.01

0.001

• 0.1

• 0.01

• 0.001

Exponents

4

What are the parts of a power?

Multiple Choice

Which number is the BASE?
2³ = 8

• 2

• 3

• 8

Use your calculator to simplify each expression.

Be careful, look out for parentheses and negative signs!

Multiple Choice

$$4^{3\ }$$  

Write in expanded form:

• 4x4x4

• 4+4+4

• 3x3x3x3

• 3+3+3+3

Fill in the Blank

$$4^3$$  

Evaluate

Multiple Choice

$$2^4$$  

Write in expanded form:

• 4x4

• 4+4

• 2x2x2x2

• 2+2+2+2

Fill in the Blank

$$2^4$$  

Evaluate

Multiple Choice

Simplify the following:

x ∙ x ∙ x ∙ x ∙ x ∙ x

• x⁶

• 6x

• x³

• 6x⁶

order of operations

​also known as GEMDAS

Grouping Symbols – () , {},[]

Exponents -  2^3 5^1

Multiplication / Division from Left to Right

Addition / Subtraction from Left to Right

5

GEMDAS are the rules we use to simplify or evaluate complicated numerical expressions.

GEMDAS

• G - grouping

• E - exponents

• M - multiplication

• D - Division

• A - Addition

• S -

Fill in the Blank

What does the S in GEMDAS stand for?

Fill in the Blank

What does the S in GEMDAS stand for?

Grouping

Anytime we have parenthesis in a problem, must solve the part of the problem that in those parenthesis. We still follow the rules of GEMDAS when solving the inside problem.

Example: 2 x (3 + 4 x 2)

We have to start with the part of the problem inside the grouping part. But we must still follow GEMDAS and solve the multiplying part of the group, then add. Once we finish the grouping, then we multiply the outside number.

Multiple Choice

Which operation is performed FIRST?

(13 - 1) + 4

• addition outside of grouping symbols

• subtraction inside of grouping symbols

• multiplication by grouping symbols

Multiple Choice

(24 - 16) ÷ 8 =

• 8

• 1

• 2

• 7

Exponents

Multiple Choice

3⁴ Which number is the base?

• 3

• 4

Multiple Choice

Write with an exponent: $$3\cdot3\cdot3\cdot3\cdot3$$  

• $$3^5$$  

• $$5^3$$  

Multiple Choice

Which is equivalent to 5 x 5 x 5 x 5

• 5³

• 5⁴

• 4⁵

• 5⁵

Multiple Choice

2⁴=?

• 4

• 6

• 8

• 16

Multiple Choice

The M and D in PEMDAS stand for Multiplication and Division.

Which operation do you do first?

• Multiplication

• Division

• Whichever comes first in the expression as you read it from left to right

Multiple Choice

The A and S in PEMDAS stand for Addition and Subtraction.

Which operation do you do first?

• Addition

• Subtraction

• Whichever comes first in the expression as you read it from left to right

Multiple Choice

What is the first step in the problem shown? 

• Multiplication

• Addition

Multiple Choice

Which operation would you do first in the following equation?

10 - 4 ÷ 1 x 5

• Subtraction

• Division

• Multiplication

• Addition

Multiple Choice

Solve This Expression - 
( 7 x 3 ) + 9

• 29

• 30

• 31

• 32

Multiple Choice

4 x 6 -2 =

• 20

• 24

• 22

• 18

Multiple Choice

Who is correct?

Sallie

$$16\div2\times8=64$$  

Brian

$$16\div2\times8=1$$  

• Sallie

• Brian

• I'm not sure

• Both

Multiple Choice

What do we do first in this problem?

3 + (4)(5) - 6 ÷ 2

• 3 + (4)

• (4)(5)

• (5) - 6

• 6 ÷ 2

Multiple Choice

Solve

3 + (4)(5) - 6 ÷ 2

• 18

• 19

• 20

• 21

Spiral Review

6

Multiple Choice

Is 5,678,987 divisible by 2?

• YES! Because I looked at the last digit and it i EVEN!

• NO! Because I looked at the last digit and it is ODD!

Multiple Select

Choose the number that is divisible by 2

• 134

• 2351

• 1256

• 4568

• 234

Multiple Select

Choose the number that is divisible by 2

• 1023

• 2348

• 3002

• 59980

• 2347

Multiple Select

Choose the number that is divisible by 3

• 954

• 295

• 859

• 219

• 1824

Multiple Select

Choose the numbers that is divisible by 3

• 124

• 234

• 562

• 2466

• 2436

Multiple Select

Choose the number that is divisible by 5

• 2345

• 1230

• 12346

• 12567

• 22345

Multiple Select

Choose the number that is divisible by 5

• 23456

• 656780

• 456784

• 345675

• 765889

WHAT IS A FACTOR ?

• a number that divides into another number exactly, without leaving a remainder

• A factor is a number when multiplied with another number produces a given number

7

What is a Factor?

• Factors are a set of all pairs of numbers that when multiplied together make a larger number.

• Example: Factors of 24

• 1 x 24

• 2 x 12

• 3 x 8

• 4 x 6

Methods to Find the Factors of a Number

• A table

• A list

• Rainbow method

• Array Model

Factor Rainbow

Start with the number x 1

Keep going until you start repeating

Take a look at the factors of 72

1x72

2x36

3x24

4x18

6x12

8x9

Multiple Select

Which of the following numbers are factors of 8? Select ALL that apply!

• 1

• 2

• 3

• 4

• 8

Factors of 8

Multiple Select

Which of the following numbers are factors of 16? Select ALL that apply! (When you are done, see if you can find more factors!)

• 2

• 3

• 4

• 5

• 8

Match

Match the following factor pairs to the whole number.

• 19

• 35

• 72

• 50

• 44

1 x 19

7 x 5

36 x 2

10 x 5

4 x 11

• 1 x 19

• 7 x 5

• 36 x 2

• 10 x 5

• 4 x 11

Multiple Select

Select All that Apply

What are multiples of: 9

• 18

• 72

• 63

• 43

Multiple Choice

What are the FIRST 5 multiples of: 5

• 5, 10, 12, 20, 135

• 5, 10, 15, 20, 25

• 5, 10, 15, 20, 22

• 2, 5, 7, 10, 15

Multiple Select

Select ALL that Apply:

What are multiples of: 7

• 42

• 27

• 49

• 63

Multiple Choice

45 is ________ of 9

• Factor

• Multiple

• Factor Pairs

Multiple Choice

5 is a ________ of 25

• Factor

• Multiple

• Factor Pairs

Multiple Choice

70 is a ________ of 10

• Factor

• Multiple

• Factor Pairs

Prime & Composite Numbers

8

​Prime Numbers

​Prime numbers are numbers greater than 1 that has exactly two factors, one, and itself.

​

​For example:

Multiplication fact of 5:

​Factors of 5:

​1, 5

​5 is a prime number.

​Composite Numbers

​Composite numbers are numbers greater than 1 that has more than two factors.

​

​For example:

​Multiplication facts of 6:

​Factors of 6:

​1, 2, 3, 6

​6 is a composite number.

​Multiplication facts of 9:

​Factors of 9:

​1, 3, 9

​9 is a composite number.

​The numbers 0 and 1 are neither prime nor composite.

Multiple Choice

Is the number 18 prime or composite?

• prime

• composite

​Prime and Composite numbers

​Prime numbers are numbers that only have two factors:	​ have more than two factors.
​Examples 3, 5, 7, 11, 31	​Examples: 6, 15, 18, 30, 100

Prime Numbers

• 2: 1, 2

• 3: 1, 3

• 5: 1, 5

• 67: 1, 67

• 89: 1, 89

• All prime numbers only have TWO factors- one and itself!

Fill in the Blank

A prime number only has ______ factors.

Multiple Select

Which numbers are prime? (Remember, prime numbers only have TWO factors, 1 and itself)

• 18

• 11

• 5

• 21

Multiple Select

Which numbers are composite? (Remember, composite numbers have 3 OR MORE factors!)

• 15

• 3

• 2

• 30

Multiple Select

Make a Factor Tree in your math journal then select the numbers that are factors of 28

• 2

• 4

• 6

• 14

• 7

​How to find the prime factorization of any number

Step 1: Find two factors for the number.

​24

​Step 2: If a factor is a prime factor, leave it there. If a factor is a composite factor, factor that again.

​_

​8

​_

​3

​Step 3: Repeat steps 1 and 2 until all factors are prime numbers.

​_

​_

​_

​2

​4

​3

​_

​_

​_

​_

​2

​2

​2

​3

Once you have all of the factors prime, you found the prime factorization!

​The prime factorization of 24 is:

​(The factors can be rearranged in a different prime factorization of the same number.)

Prime Factorization

Multiple Choice

Express 3  $$\times$$  7  $$\times$$  7  $$\times$$  3  $$\times$$  7 in exponential form.

• 3²  $$\times$$  7³

• 7²  $$\times$$  3³

• 3⁷  $$\times$$  2³

Multiple Choice

Express 5  $$\times$$  5  $$\times$$  5  $$\times$$  7 in exponential form.

• 7³  $$\times$$  5

• 5³  $$\times$$  7

• 5⁷  $$\times$$  3

A Product of Primes

•Every composite number can be expressed as a product of prime numbers.

​•This is called prime factorization.

​

15 is a composite number.

It can be written as a product of primes: 3 x 5

Some text here about the topic of discussion

​Example

To find the prime factorization:

1. Divide the number by the first prime number possible.

2. Circle the prime number, and continue with the other factor.

3. Divide the new factor by a prime number.

4. Continue this process until the only numbers you have left are prime numbers.

​Example: Prime Factorization of 32.

Multiple Choice

Use a number tree to find the prime factorization of 18

• 3 x 3 x 2

• 3 x 3 x 3

140 =2 x 2 x 5 x 7

140 = now with an exponent

2^{2 x 5 x 7}

Multiple Choice

prime factorization

• the act of breaking a number down into all of its prime factors.

• to add all numbers together

Multiple Choice

7 x 2 x 2 x 2 is the prime factorization for which of the following?

• 72

• 56

• 44

Multiple Choice

What is the prime factorization of 24?

• 2x2x2x2x3

• 2x2x3

• 3x3

• 2x2x2x3

Multiple Choice

What is the prime factorization of 8?

• 2x4

• 2x2x2

• 2x2x2x2

• 8x1

Fill in the Blank

What is the greatest common factor of 12 and 30?

9

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Fill in the Blank

What is the greatest common factor of 18 and 4?

Fill in the Blank

What is the greatest common factor of 12 and 16?