310 wholenumbers 08-14-12 handout

7/30/2019 310 WholeNumbers 08-14-12 Handout

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10

11

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Each group of three digits isseparated by a space or a comma

These groups are called periods

Each period has a name

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9 319 215

14

9 319 215

15

872 326 759 387 215

16

872 326 759 387 215

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3/12

19

US population recently

314,160,797

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21

22

23

24

25

If we label our steps the numbers

form a number line.

6 + 3 = 9

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Commutative Property

6 + 3 = 3 + 6

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Associative Property

(4 + 2) + 3 = 4 + (2 + 3)

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Identity Property

8 + 0 = 8

Closure Property

Whole Number

+ Whole Number

Whole Number

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The use of place values means that

we have to add digits according totheir place value

Tens add to tens, hundreds tohundreds, just like

You add dollars to dollars and

pennies to pennies.

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Addition, subtraction,multiplication, and division are

binary operations,

Meaning that we can work with

only two numbers at a time

As we shall see we actually will

work with only two digits at a time.

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Line up place values and add

vertically starting at the rightmostcolumn.

32

47

+ 25

72

Carry

7 ones + 5 ones = 12 ones(1 ten and 2 ones).Put the 2 in the ones placeCarry the 1 ten to the nextcolumn

1 ten + 4 tens + 2 tens = 7 tens

33

34

35

At the bookstore you spend $65 on amath book, $88 on art books and $19

on supplies. What is the total cost?

At a clothing store you spend $69 on asweatsuit, $29 for tennis shoes and $3

for socks. What is the total bill?

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If we have a board that is 9 feet

long and we remove 3 feet how longis it.

9 - 3 = 6

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To subtract large numbers

Write in column form

Subtract starting with ones column

When the lower digit is larger than

the upper the numbers cant be

subtracted

Borrow 1 from the next column and

and add 10 to upper digit

The result is called the difference

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39

4 12

Borrow 1 ten from the 5 tens, leaving 4 tens

Add the 1 ten borrowed to the 2ones, to get 12 ones

Now subtract

12 ones 7 ones = 5 ones

4 tens 1 ten = 3 tens

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41

42

Definitely not Commutative

7 - 3 3 - 7

Subtract A from B, or A less

than B means: B A.

Definitely not Associative

(7 - 4) - 1 7 - (4 - 1)

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Identity Property

8 - 0 = 8

Not Closed either

Whole Number

- Whole Number

Whole Number

only sometimes

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At the start of your vacation, the

odometer in your car reads 55743.When you return it reads 56891.

How many miles did you travel?

If you earn $750 per week, but have$123 in deductions, how much is

your take-home pay?

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Multiplication is repeated addition. The resultfrom multiplication is called the product.

If you knock down 9 bowling pins 6 frames in a

row, how many total pins did you knock down?

9 + 9 + 9 + 9 + 9 + 9 = 54

! ! or 6 9 = 54

! factors! product46

Commutative Property

3 7 = 7 3

Associative Property

(2 1) 4 = 2 (1 4)

Identity Property

8 1 = 8

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Zero Property

8 0 = 0

Closure Property

Whole Number

Whole Number

Whole Number

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To multiply large whole numbers

Write in column form

Write the number with the mostdigits on top

Multiply starting with ones column

When the product is larger than 10

carry the tens digit

Use the carried digit to add to the

next product

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50

51

52

53

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2 10 = 20

2 100 = 200

2 1000 = 2000

137,452 10,000 = 1374520000 = 1,374,520,000

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If your car needs tires and each tirecosts $63, how much will all 4 tires

cost?

If you have three $50 bills, seven $20

bills, nine $10 bills, six $5 bills andseventeen $1 bills, how much cash do

you have?

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Think of division according to its name -

dividing something into equal sized pieces.

If I have 30 marbles I can divide them into

4 groups of 7 marbles with 2 remaining.

You cannot divide 30 marbles into groups

of 0 marbles.

You REALLY cannot divide by 0.

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484

58

4

21

848

4

4

059

6

957

54

3

60

13

94912345

117

64

52

125117

8

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If you drove 637 miles in 13 hours,

how many miles did you travel perhour?

You brothers loans you $375 at no

interest. If you pay off the loan withequal monthly payments over a

year, how much would you pay eachmonth?

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When working with large numbers weoften have more digits then we really

care about.

Rounding is the process of replacing

the exact number with one that is

close enough to work with.

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If we plot 15,275 on the number line

we see that 15,275 is closer to

15,000 than to 16,000.

Therefore 15,275 rounded to thethousands would be 15,000.

15,000 16,000 17,000

15,275

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If we look closer

we see that 15,275 is closer to15,300 than to 15,200.

Therefore 15,275 rounded to thehundreds would be 15,300.

15,200 15,300 15,400

15,275

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Locate the rounding digit (mark it)

Locate the test digit (to the right of therounding digit).

If the test digit is 5 round up.

If test digit is < 5, round down.

Zero all digits to the right of therounding digit.

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Round 63,427 to the nearesthundred.

Round 76,003 to the nearest tenthousand.

Round 1,259,561 to the nearest

thousand.

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Estimation is used to find anapproximate answer.

One method of estimating uses FrontEnd Rounding. In this case each

number, including the answer, isrounded to its largest place value.

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Use Front End Rounding to estimate

3,714 + 2,489 + 781 + 5,500 + 303

5,284 + 1,376 + 450 + 9,527 + 603

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In the same way that multiplication was

shorthand for repeated addition anexponent is used to indicate repeated

multiplication. The exponent tells howmany times the base is used as a factor.

23 = 2 2 2

2 is the base and 3 the exponent

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39 is read as 3 to the ninth power

33 can be read as 3 cubed or 3 tothe third power

32 can be read as 3 squared or 3 to

the second power

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63 = (6 6 6)

74 = (7 7 7 7)

35 = (3 3 3 3 3)

02 = 0 0

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12 = 1

22 = 4

32 = 9

42 = 16

52 = 25

62 = 36

72 = 49

82 = 64

92 = 81

102 = 100

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Roots are the inverse of exponents.

Remember two squared, 22 = 4

We say that 2 is the square root of 4

If we multiply the square root by

itself (square it) we get the originalnumber

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2 is read as square root of 2

2 where the bar covers thenumber is better, and

2 where the number is

inside the radical is best

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1 = 1

4 = 2

9 = 3

16 = 4

25 = 5

36 = 6

49 = 7

64 = 8

81 = 9

100 = 10

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Please Excuse My DearAunt Sally

Parenthesis

Exponents and Roots

Multiplication and Division (L->R)

Addition and Subtraction (L->R)

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The only difference below is the order

of operations.

The one on the left is correct.

48 6 2 =

= 8 2 = 48 12

= 16 = 4

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Multiplication and division are always

done left to right.

Multiplication is commutative and

associative, but division is not.

Therefore, you can do problems that

only contain multiplication in anyorder, but if there is division then theorder is important.

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80

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Write each step out completely under

the previous step.

If you skip writing all steps, you willmake mistakes.

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12 - 4 8= 8 8

= 64

12 2 3

= 12 6

= 2

15 - 3 + 5= 15 - 8

= 7

3 5 - 7 8

= 15 - 7 8

= 8 8

= 64

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Exponents are done before

multiplication and division.

A root is an exponent and also donebefore multiplication, division,

addition or subtraction.

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5 (22) - 6

18 + 4 (8 - 3)

4 [ 2 + (9 - 5)]

52 - (4 - 3)2

(5-2) (10-7)

5 (8/2)

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Always do parentheses or othergrouping symbols first.

If there are nested groups, work

from the inside out.

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4 + 2(4 + 2(1 + 2)) = Work the insideparenthesis first

4 + 2(4 +2(3)) = Do multiplicationbefore addition

4 + 2(4 + 6) = Then the next set ofparenthesis

4 + 2(10) = Multiply before

adding

4 + 20 =

24 =

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24-4

2-7

= (24 - 4) (2 - 7)

= 20 (2 + -7)

= 20 -(7 - 2)

= 20 -5

= -4

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Step 1: Understand

Read carefully. Underline or circle

key words and numbers. This is theMOST IMPORTANT STEP.

Step 2: Plan

Decide what operations are needed to

solve the problem. Plan your work,

trying to find any patterns.

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Step 3: Solve

Use your understanding of the

problem and your plan to solve theproblem.

Step 4: Check

Read your answer within the context

of the problem. Does it make sense?

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Understand

Devin has 3 times as many CDs as

Arlene.

Devin has 36 CDs

How many does Arlene have?

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Plan

Devin has 3 times as many.

I must divide by 3 to find how many

Arlene has.

Solve

36 3 = 12

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Check

Devin has 3 times as many as Arlene

So Devin should have 3 12 = 36

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97

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100

101

102

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To find the average of a list of

numbers, add the numbers anddivide by how many numbers are in

the list

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If the scores on your last four mathtests were 96, 88, 83 and 93, what is

the average of your scores?

96 + 88 + 83 + 93 = 360

360 / 4 = 90

105

The Houston Texans scored

24,36,13,10 and 7 points in theirlast five games, what is their

average points per game?

24 + 36 + 13 + 10 + 7 = 90

90 / 5 = 18

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310 wholenumbers 08-14-12 handout

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