McGraw-Hill/Irwin ©2011 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 ©2011 The McGraw-Hill Companies, All Rights Reserved

1. Use place values to read and write numeric and verbal whole numbers

2. Round whole numbers to the indicated position

3. 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

1-2

McGraw-Hill/Irwin ©2011 The McGraw-Hill Companies, All Rights Reserved

1. Add whole numbers; check and estimate addition computations

2. 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

1-3

McGraw-Hill/Irwin ©2011 The McGraw-Hill Companies, All Rights Reserved

1. Multiply whole numbers; check and estimate multiplication computations

2. 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

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Figure 1.1

Whole-number place-value chart

Hu

nd

red

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Hu

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red

tri

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Ten

Th

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s

Hu

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red

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ousa

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s

Th

ousa

nd

s

Hu

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red

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Com

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Ten

tri

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Tri

llio

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Ten

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lion

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Bil

lion

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Com

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mil

lion

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Ten

mil

lion

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Mil

lion

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Com

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Com

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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

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Hu

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Ten

Th

ousa

nd

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Hu

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ousa

nd

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Th

ousa

nd

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Hu

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Com

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Ten

tri

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Tri

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Hu

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mil

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Mil

lion

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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

Poi

nt

Trillions Billions Millions UnitsThousands

1-7

Converting parts to a regular whole number

2,3

Convert 2.3 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

2,300,000,000

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

7843

7843

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

8000

1-10

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

1-11

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

1-12

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

1-13

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.

1-14

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

13

130 (Minuend)

- 60 (Subtrahend)

70 Difference

Check 70+60 130

1-15

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)

1-16

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

1-17

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)

1-18

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

1-19

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

1-20

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