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McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved
Chapter 1
Whole Numbers: How to Dissect and Solve Problems
McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved
• Use place values to read and write numeric and verbal whole numbers
• Round whole numbers to the indicated position
• Use blueprint aid for dissecting and solving a word problem
Whole Numbers; How to Dissect and Solve Word Problems#1#1Learning Unit ObjectivesReading, Writing, and Rounding Whole NumbersLU1.1LU1.1
McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved
• Add whole numbers; check and estimate addition computations
• Subtract whole numbers; check and estimate subtraction computations
Whole Numbers; How to Dissect and Solve Word Problems#1#1Learning Unit ObjectivesAdding and Subtracting Whole NumbersLU1.2LU1.2
McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved
• Multiply whole numbers; check and estimate multiplication computations
• Divide whole numbers; check and estimate computations
Whole Numbers; How to Dissect and Solve Word Problems#1#1Learning Unit ObjectivesMultiplying and Dividing Whole NumbersLU1.3LU1.3
1-5
Figure 1.1
Whole-number place-value chart
Hu
nd
red
bil
lion
s
Hu
nd
red
tri
llio
ns
Ten
Th
ousa
nd
s
Hu
nd
red
Th
ousa
nd
s
Th
ousa
nd
s
Hu
nd
red
s
Com
ma
Ten
tri
llio
ns
Tri
llio
ns
Ten
bil
lion
s
Bil
lion
s
Com
ma
Hu
nd
red
mil
lion
s
Ten
mil
lion
s
Mil
lion
s
Com
ma
Com
ma
Ten
s
On
es
1 , 6 0 5 , 7 4 3 , 8 9 1 , 4 1 2
1,605,743,891,412
Dec
imal
Poi
nt
Trillions Billions Millions UnitsThousands
1-6
Writing numeric and verbal whole numbers
Hu
nd
red
bil
lion
s
Hu
nd
red
tri
llio
ns
Ten
Th
ousa
nd
s
Hu
nd
red
Th
ousa
nd
s
Th
ousa
nd
s
Hu
nd
red
s
Com
ma
Ten
tri
llio
ns
Tri
llio
ns
Ten
bil
lion
s
Bil
lion
s
Com
ma
Hu
nd
red
mil
lion
s
Ten
mil
lion
s
Mil
lion
s
Com
ma
Com
ma
Ten
s
On
es
1 , 6 0 5 , 7 4 3 , 8 9 1 , 4 1 2
One trillion, six hundred five billion, seven hundred forty three million, eight hundred ninety one thousand, four hundred twelve
Dec
imal
Poi
nt
Trillions Billions Millions UnitsThousands
1-7
Converting parts to a regular whole number
2,4
Convert 2.4 billion to a regular whole number
Step 2. Add zeros so the leftmost digit ends in the word name of the amount youwant to convert. Be sure to add commas
as needed.
Step 1. Drop decimal point and insert a comma
2,400,000,000
1-8
Rounding Whole Numbers
9362
9462
Step 1. Identify the place value of the digit you want to round
Step 2. Identify the digit to the right.If 5 or more, increase the identified digit
by 1, if less than 5 do not change
Step 3. Drop all digits to the rightof the identified digit
9400
1-9
Rounding all the way
9362
9362
Step 1. Identify leftmost digit
Step 2. Identify the digit to the right.If 5 or more, increase the identified digit
by 1, if less than 5 do not change
Step 3. Change all other digits tozero
9000
1-10
How to Dissect and Solve a Word Problem
Organization and persistence
The Facts Solving for? Steps to take Key Points
1-11
General Problem-Solving Procedure
• Step 1. State the problem(s)
• Step 2. Decide on the best methods to solve the problem(s)
• Step 3. Does the solution make sense?
• Step 4. Evaluate results
1-12
How to Dissect and Solve a Word Problem
Tootsie Roll Industries sales reached one hundred ninety-four million dollars and a record profit of twenty-two
million, five hundred fifty six thousand dollars. Round the sales and profit figures all the way.
The Facts Solving for? Steps to take Key PointsSales: One hundred ninety-four million dollars.
Profit: Twenty-two million, five hundred fifty-six thousand dollars.
Sales and profit rounded all the way.
Express each verbal form in numeric form. Identify leftmost digit in each number.
Rounding all the way means only the leftmost digit will remain. All other digits become zeros.
Sales: One hundred ninety-four million dollars. ----------->$194,000,000 -----------> $200,000,000
Profit: Twenty-two million, five hundred fifty-six thousand dollars --------> $22,556,000 ---------> $20,000,000
1-13
Adding Whole Numbers3 Steps1. Align the numbers according to
their place values
2. Add the units column. Write the sum below the column. If the sum is more than 9, write the units digit and carry the tens digit.
3. Moving to the left, repeat Step 2 until all place values are added.
Example 2 1 1
1,362
5,913
8,924
6,594
22,793
1-14
Alternative check
Add each column as a separate total and then combine. The end result is the same.
1,362
5,913
8,924
6,594
13
18
2 6
20
22,793
1-15
Estimate Addition by Rounding All the Way
Example 2 1 1
1,362
5,913
8,924
6,594
22,793
Example 211
1,000
6,000
9,000
7,000
23,000
*Final answer could have more than one non-zero since total is not rounded all the way.
1-16
Subtracting Whole Numbers
3 Steps1. Align the minuend and
subtrahend by place values2. Begin the subtraction with the
units digits. Write the difference below the column. If the units digit in the minuend is smaller than the digit in the subtrahend, borrow 1 from the tens digit in the minuend.
3. Moving to the left, repeat Step 2 until all place values in the subtrahend are subtracted
Example 12
3 2 12
4,327 (Minuend)
-1,340 (Subtrahend)
2,987 Difference
Check 2,987+1,340 4,327
1-17
Multiplication of Whole Numbers4 Steps1. Align the multiplicand and multiplier at the
right.
2. Multiplying the right digit of the multiplier with the right digit of the multiplicand. Keep multiplying as you move left through the multiplicand.
3. Your partial product right digit or first digit is placed directly below the digit in the multiplier that you used to multiply.
4. Continue steps 2 and 3 until multiplication process is complete. Add the partial products to get the final product.
Example
418 (Multiplicand)
x 52 (Multiplier)
836
20 90 (Partial Product)
21,736 (Product)
1-18
Checking and Estimating Multiplication
Check
52
x 418
416
52
20 8
21,736
Estimate
50
x 400
20,000
Check the multiplication process by reversing the multiplicand and multiplier and then multiplying
1-19
Multiplication Shortcut with Numbers Ending in Zero
3 Steps1. When zeros are at the end of the
multiplicand or the multiplier, or both, disregard the zeros and multiply
2. Count the number of zeros in the multiplicand and multiplier. (4)(4)
3. Attach the number of zeros counted in Step 2 to your answer
Solution
65
x 42
130
260
27,3000,000000
Example
65000 (3 zeros)
x 420 (1 zeros)
(4 zeros)
1-20
Multiplying a Whole Number by a Power of 10
2 Steps1. Count the number of zeros in the power of 10.
2. Attach that number of zeros to the right side of the other whole number to obtain the answer. Insert commas as needed.
99 x 10 = 990 = 990 <----Add 1 Zero99 x 100 = 9,900 = 9,900 <----Add 2 Zero
99 x 1,000 = 99,000 = 99,000 <----Add 3 Zero
1-21
Division of Whole Numbers
• How many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient.
Example
18Quotient
Divisor 15 270 Dividend
15
120
120
0
1-22
Division of Whole Numbers
• How many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient.
Example
36 R 111 Quotient
Divisor 138 5,079 Dividend
4 14
939
828
111
1-23
Estimating and Checking Division
Example
36 R 111 Quotient
Divisor 138 5,079 Dividend
4 14
939
828
111
Check
138
x 36
828
4 14
4,968
+ 111
5,079
Estimate 50100 5,000
1-24
Division Shortcut with Numbers Ending in Zeros
2 Steps
1. Count the number of ending zeros in the divisor.
2. Drop the same number of zeros in the dividend as in the divisor, counting from right to left.
95,000 / 10 -- 95,000 = 9,500 <----Drop 1 Zero95,000 / 100 -- 95,000 = 950 <----Drop 2 Zeros95,000 / 1,000 -- 95,000 = 95 <----Drop 3 Zeros
1-25
Problem 1-40
46 1,950 184
110 92
18
42 R18Check:
46 x 42 = 1,932 + 18 (R)
1,950
Solution:
1-26
Problem 1-53:Website: Average daily unique
visitor:
1. Orbitz.com 1,527,000
2. Mypoints.com 1,356,000
3. Americangreetings.com 745,000
4. Bizrate.com 503,000
5. Half.com 397,000
1,527,000 1,356,000 745,0000 503,000+ 397,000 4,528,000 visitors
Solution:5 4,528,000
45 28 25
30 30
905,600 average
1-27
Problem 1-54:
5,000 shares bought - 1,990 shares sold 190+450+450+900= 1,990 3,010 3,010 shares x $48=$144,480
Solution:
1-28
1-63:
90 + 70 + 65 + 310 = 535 customers x $9 $4,815
Solution (a):
Solution (b):
$4,815 x 52 = $250,380
1-29
1-65:
$61,000 - 6,128 ($1,462 + $3,782 + $884)$54,872
Solution:
1-30
1-69:
$ 900 + 1,200 $2,100 - 614 ($350 + $44 + $160 + $60) $1,486
Solution:
