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Whole Numbers; How to Dissect and Solve Word Problems

Kirkwood Community CollegeJanuary 26, 2009

Presented by Sanh Tran, MBA, CPIM, CTL

McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved

Chapter 1

Whole Numbers: How to Whole Numbers: How to Dissect and Solve ProblemsDissect 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#1Learning Unit ObjectivesReading, Writing, and Rounding Whole NumbersLU1.1

1-3

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#1Learning Unit ObjectivesAdding and Subtracting Whole NumbersLU1.2

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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#1Learning Unit ObjectivesMultiplying and Dividing Whole NumbersLU1.3

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Decimal System

• U.S. numbering system: Decimal system

• Base 10 system

• Decimal point: A dividing point that separates the whole numbers from the decimal numbers.

• Example:145.79

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Figure 1.1

Whole-number place-value chart

Hun

dred

bill

ions

Hun

dred

trill

ions

Ten

Tho

usan

ds

Hun

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Hun

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Ten

trill

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Ten

bill

ions

Bill

ions

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Hun

dred

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ions

Ten

mill

ions

Mill

ions

Com

ma

Com

ma

Ten

s

One

s

1 , 6 0 5 , 7 4 3 , 8 9 1 , 4 1 2

1,605,743,891,412

Dec

ima l

Po i

nt

Trillions Billions Millions UnitsThousands

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Writing numeric and verbal whole numbers

Hun

dred

bill

ions

Hun

dred

trill

ions

Ten

Tho

usan

ds

Hun

dred

Tho

usan

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usan

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Hun

dred

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Com

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Ten

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ions

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Ten

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ions

Bill

ions

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Hun

dred

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mill

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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

Po i

nt

Trillions Billions Millions UnitsThousands

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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

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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

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Rounding all the way

93629362

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

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How to Dissect and Solve a Word Problem

Organization and persistence

The Facts Solving for? Steps to take Key Points

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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

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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

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Addition

• Addends: Numbers that are to be added together in an addition.

• Sum (Amount or total): The result of an addition.

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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

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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 2 620 22,793

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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.

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Subtraction

• Minuend: The larger number to from which to subtract another number.

• Subtrahend: The number that is to be subtracted (taken away) from another number.

• Difference: The result of a subtraction.

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Subtracting Whole Numbers3 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

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Multiplication

• Multiplicand: The top number that we want to multiply in a multiplication.

• Multiplier: The bottom number that is used to multiply another number.

• Product: The final answer (result) of a multiplication.

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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)

83620 90 (Partial

Product)

21,736 (Product)

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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

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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

Example65000 (3 zeros)

x 420 (1 zeros)

(4 zeros)

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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

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Division

• Dividend: The number that will be divided by another number.

• Divisor: The number that is used to divide another number.

• Quotient: The result of a division.• Partial quotient: Part of the result of an uneven division,

excluding the remainder.• Remainder: The leftover amount in an uneven division.

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Division of Whole Numbers

• How many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient.

Example 18 Quotient

Divisor 15 270 Dividend

15 120 120

0

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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

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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

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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

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Problem 1-40

46 1,950 184

110 92

18

42 R18Check:

46 x 42 = 1,932 + 18 (R)

1,950

Solution:

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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

Problem 1-53

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Problem 1-54: 1. Calculate shares sold:

190+450+450+900= 1,990 2. Remaining shares Lee Wong owned: 5,000 shares bought - 1,990 shares sold--------------------------- 3,010 3, Total values of Lee’s stock:

3,010 shares x $48=$144,480

Solution:

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Problem 1-56

• 90, 65, 85, 80, 75 and 90↓

• Lowest grade: 65• 90+85+80+75+90 = 420• 5 different grades• 420÷5 = 84 (average grade)

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Problem 1-63:

Total customers in the week:90 + 70 + 65 + 310 = 535 customersTotal sales for the week:

535 x $9 $4,815

Solution (a):

Solution (b):52 weeks in a year

Total sales for the year:

$4,815 x 52 = $250,380

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Problem 1-65:

1.Calculate the total deductions:$1,462 + $3,782 + $884 = 6,1282. Calculate net pay:$61,000 - 6,128_______$54,872

Solution:

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Problem 1-69:Expenses:

$350 + $44 + $160 + $60=614Deposit: 1,200 $ 900 + 1,200 $2,100 (Subtotal after deposit) - 614 (Less subtotal for expenses) $1,486

Solution:

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Reference

• Slater, J. (2008). Practical business math procedures (9th ed.). New York: McGraw-Hill/Irwin

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Homework (5 points total)

1-42 (0.5 point) 1-46 (0.5 point)

1-48(0.5 point) 1-52 (0.5 point)

1-58 (0.5 point) 1-64 (0.5 point)

1-70 (1 point) 1-76 (1 point)