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					            Whole Numbers and Decimals
Define:
 Whole Numbers
 Decimals
Read and write:
 Whole Numbers
 Decimals
Round:
 Whole Numbers
 Decimals
Add and Subtract:
 Whole Numbers
 Decimals
Order of Operations:
 By hand
 In Excel
Multiply and Divide:
 Whole Numbers
 Decimals
Omitting zeros when multiplying or dividing

           Math Word-Application Problems:
 Translating words into math symbols
 Steps to solve math word-application problems
 Estimating an answer
                                 Whole Numbers: numbers to the left of the decimal point. Uses
                                  the ten one-place digits: 0,1,2,3,4,5,6,7,8,9. No "parts of the
                                 whole", or no numbers between 1 and 0. Use a comma every
                                                            third place.
                                                     Trillions                                         Billions                                       Millions                                 Thousands                            Ones




                                                                                                                                                                                    Hundred Thousands
                                 Hundred Trillions




                                                                                                                                   Hundred Millions
                                                                                    Hundred Billions




                                                                                                                                                                                                        Ten Thousands
                                                        Ten Trillions




                                                                                                                                                          Ten Millions
                                                                                                         Ten Billions




                                                                                                                                                                                                                        Thousands
                                                                        Trillions




                                                                                                                                                                         Millions
                                                                                                                        Billions
                                                                                       4                   5             6            7                     5             8            4                  5              2
                                                                                                                                                                                                                         4

                                   Fifteen Million, Seven Hundred Eighty Nine Thousand, Four
                  15,789,458                             Hundred Fifty Eight
 Whole
                                Four Hundred Thirty Trillion, Four Hundred Fifty Seven Billion, Eight
Numbers
                                 Hundred Forty Five Million, Eight Hundred Ninety Six Thousand,
          430,457,845,896,214                          Two Hundred Fourteen
                                 Four Hundred Fifty Six Billion, Seven Hundred Fifty Eight Million,
                                 Four Hundred Fifty Two Thousand, One Hundred Nineteen And
          456,758,452,119.155                   One Hundred Fifty Five Thousandths
Decimal
                                   Two Hundred Fifty Four Thousand, Four Hundred Nineteen
Numbers
                    0.254419                                  Millionths
                                  One Hundred Fifty Four Thousand Five Hundred Eighty Seven
                 $154,587.25                       Dollars And Twenty Five Cents
                                                 Decimals: numbers to the right
 decimal point. Uses                                  of the decimal point -
                     The word                    representing parts of a whole -
,9. No "parts of the "and" goes                  "a whole" is the number 1 and
Use a comma every here when                     the "parts" is a number between
                                    you say the 1 and 0. Define Decimal ==> A
                                    word         number written with a decimal
                     Ones                            such as 4.987 or .062




                                                                                                                     Hundred-Thousandths
                                         Decimal Point (and)




                                                                                                   Ten-Thousandths
                                                                                     Thousandths
                                                                        Hundredths
          Hundreds




                                                                                                                                           Millionths
                                                               Tenths
                             Ones
                      Tens




           1          1      9                                 1         5            5
           5          6      3                                 2         5            4              4                  1                   9
    Formatting is like a façade on a house: it is only what is on top. Formatting does not necessarily refle
                                                              number
    General          Number        Currency        Accounting          Date           Time




                                                                                  Shows date
                                      Shows "floating"      Shows "fixed"         format,             Shows time
No commas,       Shows commas dollar sign,                  dollar sign,          underneath is the   format,
shows as many and as many             commas and as         commas and as         number of days      underneath is the
decimals as you decimals as you many decimals as            many decimals as      since Jan. 1,       proportion of one
type in          tell it to show      you tell it to show   you tell it to show   1900                24 hour day
     12569.45698            12,569.46       $12,569.46       $      12,569.46              7/3/2006         8:00:00 AM
     12569.45698         12569.45698       12569.45698           12569.45698                  38901       0.333333333
     12569.45698         12569.45698       12569.45698           12569.45698                  38901       0.333333333
s not necessarily reflect the underlying

              Percentage             Fraction
            Shows
            Percentage
            format (slides
            decimal to right
            two positions and
            then adds the
            percentage            Division
            symbol). What is      represented with
            underneath is a       a numerator and
            decimal or whole      a denominator
            number (.06 or 1      and a line
            ))                    between the two
                        6.00%                   1/4
                           0.06                0.25
                           0.06                0.25
          Rules for Rounding by hand
  Select the position to which you would
  like to round. We will call this the
1 "selected position".
     If you are rounding to a whole number
     draw a line under the "selected
     position".
     If you are rounding to a decimal
     position, draw a vertical line after the
     "selected position" to indicate that you
     will drop the remaining digits.
2 Look one position to the right

    If this digit is 5 or more, increase the
    digit in the "selected position" by one
    If this digit is 4 or less, DO NOT
    CHANGE the digit in the "selected
    position"
  Change all the digits to the right of the
3 "selected position" to zeros.
    If you have decimal positions that have
    zeros, you can drop them.
                                                                    by hand
  Financial Statements are often rounded
  to the Thousands position                     $5,698,700,459.25
  Income Taxes are rounded to the ones
  position                                               $555.25
  Payroll deductions are rounded to the
  hundredths position                                   $98.2569

          ROUND function in Excel

  To round to the thousands position use "-
  3" as the second function argument
   =ROUND(C2,-3)
  To round to the ones position use "0" as
  the second function argument
   =ROUND(C3,0)

  To Round to the Hundredths Position use
  "2" as the second function argument
   =ROUND(C4,2)
                                                                    ROUND function
  Financial Statements are often rounded
  to the Thousands position                     $5,698,700,459.25
  Income Taxes are rounded to the ones
  position                                               $555.25
  Payroll deductions are rounded to the
  hundredths position                                     $98.26

      Increase/Decrease decimals with
                formatting
Use the Increase/Decrease Decimal
button on the Formatting toolbar
                                                   Formatting (Façade)
Income Taxes are rounded to the ones
position                                 $555.25
Payroll deductions are rounded to the
hundredths position                     $98.2569
Name              Gross Pay     Deduction 1       Net Pay
Suix Chin              5,468.25
Stephanie Walting      7,667.54
Rachel Hensley         6,900.20
                  Totals

          Assumption
Deduction Rate               0.32

  Rule for when to use the ROUND function: If you will use the
 result of a formula in a subsequent Excel formula and you are
multiplying or dividing decimals where you are required to round
to a certain position, you must use the ROUND function to get a
                          correct answer.
In the range C4 to C6 (green color) create efficient formulas that
                                                                                                    5) Because each deducti
  calculate the deduction based on the rate in cell B10 (Gross *                                    subtracted from each pay
 deduction rate). Then calculate the net pay in the range D4:D6.                                    function. The Decimal bu
 Then add totals in cells C7 and D7. Hint: When we calculate a                                      are Rounded, but they ar
              deduction, we must round to the penny.


Name              Gross Pay     Deduction 1 Net Pay                          Name              Gross Pay
Suix Chin              5,468.25     1,749.84    3,718.41                     Suix Chin              5,468.25
Stephanie Walting      7,667.54     2,453.61    5,213.93                     Stephanie Walting      7,667.54
Rachel Hensley         6,900.20     2,208.06    4,692.14                     Rachel Hensley         6,900.20
                  Totals            6,411.51   13,624.48                                       Totals

          Assumption                                                                   Assumption
Deduction Rate                0.32                                           Deduction Rate              0.32



               1) Your boss looked at your table without the
               ROUND function

                2) and then typed the numbers she saw into the cells here.

                      3) When she added them up she got a different number than
                      you did. Her number is correct because what you see is what
                      the SUM function is adding!
5) Because each deduction is a bunch of pennies that are
subtracted from each paycheck, you must use the ROUND
function. The Decimal button on the toolbar makes it look like they
are Rounded, but they are not.



           Deduction 1 Net Pay
               1,749.84    3,718.41
               2,453.61    5,213.93
               2,208.06    4,692.14
               6,411.52   13,624.47


                                           1,749.84000
                                           2,453.61280
                 1749.84                   2,208.06400
                 2453.61
                 2208.06
                 6411.51



                             4) In your original calculations, if you increase your decimals, you
                             can see there are some decimals that you originally could not
                             see, but the SUM function does see them. The SUM function
                             sees them and used them when it adds. That is why your SUM
                             shows 6,411.52 (it has more decimals to add and so it gets one
                             penny more).
                                         Whole Numbers
       16
+      15




       62
-      43




                                             Decimals
    16.256
+   15.128




     62.07
-    43.29

                                                         Whole
                     Income From Bookkeeping            15,580.00
                     Income From Tax Preparation        11,504.00
             add     Total Revenue

                      Rent Expense                       1,000.00
                      Insurance Expense                  1,300.00
                      Salary Expense                     3,145.00
                      Supplies Expense                     526.00
                      Depreciation Expense                 244.00
             add      Total Expenses
             subtract Net Income
s




                                  Decimals
    Income From Bookkeeping       15,580.58
    Income From Tax Preparation   11,504.19
    Total Revenue

    Rent Expense                   1,000.12
    Insurance Expense              1,300.26
    Salary Expense                 3,145.37
    Supplies Expense                 526.86
    Depreciation Expense             244.86
    Total Expenses
    Net Income
Name   Gross Pay     Deduction 1      Deduction 2      Deduction 3        Total Deductions
Name 1        881.13            13.06            12.94              29.76
Name 2        690.13            24.94            12.58              20.38
Name 3       1086.01            18.26             26.8               24.8
Name 4        672.43            19.99            25.02              25.56
Name 5        937.85            25.66            21.59              14.08
Name 6        994.07            31.72            14.94              29.51
Name 7       1005.24            16.27            35.35              37.27
Name 8        988.26             24.7            27.42              29.17
Name 9        688.82            37.78            15.61              15.62
Totals       7943.94          212.38            192.25             226.15

Name   Gross Pay     Deduction 1      Deduction 2      Deduction 3        Net Pay
Name 1        881.13            13.06            12.94              29.76
Name 2        690.13            24.94            12.58              20.38
Name 3       1086.01            18.26             26.8               24.8
Name 4        672.43            19.99            25.02              25.56
Name 5        937.85            25.66            21.59              14.08
Name 6        994.07            31.72            14.94              29.51
Name 7       1005.24            16.27            35.35              37.27
Name 8        988.26             24.7            27.42              29.17
Name 9        688.82            37.78            15.61              15.62
Totals       7943.94          212.38            192.25             226.15


                                                       Name                Gross Pay
                                                       Suix Chin                        5,468.25
                                                       Stephanie Walting                7,667.54
                                                       Rachel Hensley                   6,900.20
                                                                           Totals

                                                                        Assumption
                                                       Deduction Rate                        0.32
Net Pay




               efficient formula
=B15-SUM(C15:E15)
               inefficient formula
=B16-C16-D16-E16




Deduction 1     Net Pay
       1,749.84               3,718.41
       2,453.61               5,213.93
       2,208.06               4,692.14
       6,411.51              13,624.48
  d67cc0eb-3fd2-449d-8e1c-09d4495967ae.xls - Order of Operations


Arithmetic operation signs in Excel:
( ) represents Parentheses
^ represents Exponents (powers and roots)
* represents Multiplication
/ represents Division
+ represents Addition
– represents Subtraction

Order of Operations form Algebra class (Each one is left to right):
Please  Parenthesis  ( )
Excuse  Exponents  ^  2^2 = 4 or 4^(1/2) = 2
My Dear  Multiplication  * and Division  /
Aunt Sally  Adding (SUM)  + and Subtraction  -



Excel's Order of Operations:
Parenthesis ( )
Ranges use of colon symbol ":"
  Example: =SUM(A1:A4)
Evaluate unions (,)
  Example: =SUM(A1:A4,B2:C7)
Negation (-)
  Example: =-2^4  16
  Example: =-(2^4)  -16
Converts % (1%  .01)
Exponents (^)
  Example 1: 4^(1/2) = 2
  Example: 3^2 = 9
Multiplication (*) and division (/), left to right
Adding (+) and division (-), left to right
Text operators (&  Concatenation)
Comparative symbols: =, <>, >=, <=, <, >
If anything is still left, then left to right


                               Page 15 of 29
     d67cc0eb-3fd2-449d-8e1c-09d4495967ae.xls - OOO (2)


3+3*2       =D1+E1*F1                         3   3   2
(3+3)*2     =(D2+E2)*F2                       3   3   2
2+(2+1)*3   =D3+(E3+F3)*G3                    2   2   1   3

2-1+(3-1)*2 =D4-E4+(F4-G4)*H4                 2   1   3   1   2




                       Page 16 of 29
                                                Multiplying Whole Numbers
       690
*       43                   3                                                                         4
                             2                                                                         6
                             690 multiplicand factor                                                   6
                         x    43 multiplier factor                                                     4
                            2070 partial product (3 x 69)
                        + 27600 partial product (4 x 69)                                               2
                           29,670 product (answer)                                                     8
                                                                                                       3
                                                                                                       5
                                                                                                       3
       300                  300       2 zeros
*       70                 x 70       1 zero
                            21 +      3 zeros
                           21,000      answer

                         Omitting zeros when multiplying: "remove at
                         beginning, add back at end"




                                                 Dividing Whole Numbers
       256
                                                            4   Numerator = Dividend
      16
                                                            2   Denominator = Divisor

                                                            4 (Numerator)  2 (Denominator) = 2 (Quotient or answer)

                                                            2 (Denominator)     4 (Numerator)
     108000
      900                                                 Zeros in division:
                                                            0/4 = 0 because 0 * 4 = 0
                                                            however
                                                            4/0 = ? = in not defined because what?*0 = 4 ????
      1080
                                                            Reciprocals: 1/2 and 2/1 are reciprocals
       9
              Omitting zeroes in division

              108000  900 = 1080 9 = 120                                             876
                                                                                          2

                                                                                          2

                                                                                          3




                  Multiply Decimals

     0.032          Items      Boomerangs
*    0.070          Quantity          5.00
                          Price              22.25
                          Total

                          Hours              39.50                    Gross                -
                          Wage               15.75                    Tax Rate            0.06
                          Gross                                       Tax Rate


                          Divide Decimals

                 17.60
                 0.25



                  17.6 .25 = 1760 25 = 70.4


               1,760.00
                 25.00


                                            When the denominator is
                 15.00                      between 1 and 0, the quotient
                                            will always be bigger than the
                 0.25
                                            Numerator




Different ways to express quotient:                                Quick way to estimate
                       20                                                   29548 round up ==>
                      15                                          *          0.10 slide decimal to right
               1.333333     1R5         1 1/3
              Decimal     Remainder Fraction                          slide decimal back to left <==
                              158   56,986
                              190       23
                              197




r) = 2 (Quotient or answer)




ause what?*0 = 4 ????
30000
    1
30000
 3000
         Steps for solving word-application problems:
                Read problem carefully – be sure you know what
Step 1                            they are asking.
               List all relevant facts. List all information you want
Step 2                                 to find.
Step 3                      Estimate reasonable answer.
Step 4                     Set up the problem and solve.
Step 5                          Check your answer.
                 Write answer in words – go back and use the
Step 6                  nouns and verbs from the problem.


  Short list of steps for solving word-application problems:
Step 1           Read problem carefully and list all relevant facts
Step 2           Set up problem, solve, check and double check
                  Write answer in words – go back and use the
Step 3                 nouns and verbs from the problem.

                                  Translate words into math symbols
Add            Subtract            Multiply       Division        Equal         Powers
plus           less                product        divided by      is            squared
more           subtract            double         divided into    the same as   raised to
more than      subtracted from     triple         quotient        equals        to the second power
added to       difference          times          goes into       equal to      cubed
increased by   less than           of             divide          yields        to the 12th power
sum            fewer               twice          divided equally results in
total          decreased by        twice as much per              are
sum of         loss of
increase of    minus
gain of        take away
add            reduced by


  The three invoices each had a total of $14.26
listed on the bottom line. What is the total that is
                      owed?
  If the total gross earnings for the year were
$29,013.45 and the first $15,000 of those gross
  earnings were taxed at a rate of .10 and the
remaining amount was taxed at .15. What is the
   total tax paid for the year if you round your
               answer to the dollar?
1)                              Setup for Math Problems In Excel
2)
3)
4)
5)
6)
7)
8)
9)

     If there are 10 Boomerangs for sale at $20 each and the cost for
        each boom is $10, what is the total profit if you sell them all?
                             Summary Exercise
Step 1         Read and list all relevant facts
           1   Average wedding costs in USA in 2004
           2   Cost of average 2001 wedding =                  $20,357.00
               Average cost has increased as the average
               number of wedding guest has grown to over
           3   200
           4   Graph shows details
                 Wedding reception                              $9,590.00
                 Rings (engagement and wedding)                 $5,099.00
                 Photographer                                   $1,647.00
                 Misc. expense                                  $1,583.00
                 Wedding dress and headpiece                    $1,242.00
                 Music                                          $1,042.00
                 Bridesmaids' dresses (5)                         $992.00
                 Bouquets and other flowers                       $950.00
                 Rehearsal dinner                                 $877.00
                 Men's formal wear                                $849.00
                 Mother's of the Bride apparel                    $297.00

Step 2 and 3
a            The total Costs shown in the graph =

               The increase in the average wedding cost in
b              2004 over the cost in 2001 =

c              Our cost for wedding =                           $7,000.00
               Cost per guest =                                    $32.00
               The number of guests we can invite =
               Since we can not invite a part of a guest, we
               must round ==>
               Total costs for us =
               Amount left over =

               Number of guests that are invited to wedding
d              =                                                      150
               Budgeted amount for wedding =                    $7,000.00

               Amount that can be spent on each person =
               Round to the nearest cent =

e              Budgeted amount for wedding =                    $4,000.00
               Cost per guest =                                    $27.00
               The number of guests we can invite =
               Since we can not invite a part of a guest, we
               must round ==>
               Total costs for us =
               Amount left over =

f              Budgeted amount for wedding =                    $1,000.00
               Cost per guest =                                    $15.00
               The number of guests we can invite =
    Since we can not invite a part of a guest, we
    must round ==>
    Total costs for us =
    Amount left over =

g   Number of bridal party bouquets =                     5
    Cost per bridal party bouquets =                 $36.25
    Number of boutonnieres =                              5
    Cost per boutonnieres =                           $7.50
    Total amount budgeted for flowers =             $863.00
    Amount spent for bridal party bouquets and
    boutonnieres =
    Amount left over
                                                                            s
#1   Round to the nearest ten
     number to round =                                              844
     Answer =                                                       840

#2   Round to the nearest hundred
     number to round =                                            21,958
     Answer =                                                     22,000

#3   Round to the nearest thousand
     number to round =                                           671,529
     Answer =                                                    672,000

#4   Front End Round
     number to round =                                            50,987
     Answer =                                                     50,000

#5   Front End Round
     number to round =                                           851,004
     Answer =                                                    900,000

#6                         Commissions Earned
     Monday                                                      $124.00
     Tuesday                                                      $88.00
     Wednesday                                                    $62.00
     Thursday                                                    $137.00
     Friday                                                      $195.00
     Total =                                                     $606.00

                                                     The total
                                                     commissions that
                                                     Suzanne earned =
     Answer =                                        $606.00

#7   Total Costs
     Cost per airless sprayer =                                $1,540.00
     Number of airless sprayers purchased =                            3
                                         Total =               $4,620.00
     Cost per rototillers =                                      $695.00
     Number of rototillers purchased =                                 5
                                         Total =               $3,475.00
     Cost per ladders =                                           $38.00
     Number of ladders purchased =                                     8
                                         Total =                 $304.00

                         Total for all purchases =             $8,399.00

#8   Round to the nearest cent                                         2
     Number                                                      21.0568
     Answer =                                                     $21.06

#9   Round to the nearest cent                                          2
    Number                                           364.345
    Answer =                                         $364.35

#10 Round to the nearest cent                               0
    Number                                            7246.49
    Answer =                                        $7,246.00

#11 add                                                   9.6
                                                        8.42
                                                       3.715
                                                       159.8
                                          Total =    181.535

#12 add                                                2.715
                                                       32.78
                                                       426.3
                                                          37
                                          Total =    498.795

#13 Subtract                                           341.4
                                                       207.8
                                   Difference =        133.6

#14 Subtract                                              3.8
                                                      0.0053
                                   Difference =       3.7947

#15 Multiply                                           21.98
                                                         0.72
                                       Product =     15.8256

#16 Multiply                                           218.6
                                                       0.037
                                       Product =      8.0882

#17 Division
    Numerator (Dividend)                             252.008
    Denominator (Divisor)                               21.8
                                       Quotient =      11.56

#18 Division
    Numerator (Dividend)                              57.358
    Denominator (Divisor)                               2.41
                                       Quotient =       23.8

#19 Division
    Numerator (Dividend)                              79.135
    Denominator (Divisor)                              18.62
                                                        4.25

#20 Total costs
    Number of solvent gallons to buy                     32.6
    Solvent cost per gallon                            $13.48
                                           Total =    $439.45
    Number of acid gallons to buy                        18.5
    Acid cost per gallon                                $3.56
                                           Total =     $65.86
    Total for solvent and acid =                      $505.31

#21 Total costs
    Roof Materials per 10x10 squares                    $84.52
    Installation labor per 10x10 squares                $55.75
    Supplies per 10x10 squares                           $9.65
    Total Costs per 10x10 square                       $149.92
    Number of 10x10 squares                               26.3
    Total costs                                      $3,942.90


#23 How much change was received
    Number of meters of electrical wire
    purchased                                            16.5
    Electrical wire cost per meter                      $0.48
    Number of meters of brass rod                           3
    Cost of brass rod per meter                         $1.05
    Total cost                                         $11.07
    Amount of one fiver                                 $5.00
    Number of fivers                                        3
    Total amount of money given to cashier             $15.00

    Amount of change he got from three fivers =         $3.93

#24 Price of bananas per pound
    Price of bananas per kilogram                       $1.74
    Number of pounds in one kilogram                      2.2
    Price for 2.2 pounds of banana                      $1.74
    Price per 1 pound of banana                         $0.79

#25 Find Number of seedlings
    Ounces of concentrated fertilizer needed for
    one seedling                                        0.058
    Ounces of concentrated fertilizer available
    for use                                            14.674
    Number of seedlings that can be fertilized       253.0000
   50,000



  900,000




The total commissions that Suzanne earned = $606.00

				
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