Chapter OneWHOLE NUMBERS: HOW TO DISSECT AND SOLVE

WORD PROBLEMS

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Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

LU 1-1: Reading, Writing, and Rounding Whole Numbers

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.

LU 1-2: Adding and Subtracting Whole Numbers

4. Add whole numbers; check and estimate addition computations.

5. Subtract whole numbers; check and estimate subtraction computations.

LU 1-3: Multiplying and Dividing Whole Numbers

6. Multiply whole numbers; check and estimate multiplication computations.

7. Divide whole numbers; check and estimate computations.

LEARNING UNIT OBJECTIVES

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WHOLE NUMBER PLACE-VALUE CHART

1,605,743,891,412 displayed on the Whole Number Group Chart:

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WRITING NUMERIC AND VERBAL WHOLE NUMBERS

1,605,743,891,412 verbalized:

One trillion, six hundred five billion, seven hundred forty-three million, eight hundred ninety-one thousand, four hundred twelve

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CONVERTING PARTS TO A REGULAR WHOLE NUMBER

Convert 2.3 million to a regular whole number.

2,300,000Step 2. Add zeros so the left most digit ends in the word name of the amount you want to convert. Be sure to add commas as needed.

Step 1. Drop the decimal point and insert a comma.

2,3

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ROUNDING WHOLE NUMBERS

9400Step 3. Drop all digits to the right of the digit you want to round.

Step 1. Identify the place value of the digit you want to round.

9362

Step 2. Identify the digit to the right. 9362

If 5 or more, increase the identified digit by 1, if less than 5 do not change.

9462

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ROUNDING ALL THE WAY

Step 2. Identify the digit to the right. 7843

8000

Step 3. Change all other digits to zero.

If 5 or more, increase the left-most digit by 1; if less than 5, do not change.

7843

Step 1. Identify the left most digit. 7843

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HOW TO DISSECT AND SOLVE A WORD PROBLEM

Organization and persistence

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GENERAL PROBLEM-SOLVING PROCEDURE

Step 1. State the problem(s).

Step 4. Evaluate results.

Step 3. Does the solution make sense?

Step 2. Decide on the best method(s) to solve the problem(s).

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HOW TO DISSECT AND SOLVE A WORD PROBLEM

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

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.

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ADDING WHOLE NUMBERS

3 Steps1. Align the numbers according

to their place values.

Example 1,362

5,913

8,924

6,594

22,793

3. Moving to the left, repeat Step 2 until all place values are added.

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.

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ALTERNATIVE CHECK

Ones Column 2 + 3 + 4 + 4 13

Tens Column 6 + 1 + 2 + 9 18

Hundreds Column 3 + 9 + 9 + 5 26

Thousands Column 1 + 5 + 8 + 6 20

22,793

1,362

5,913

8,924

6,594

Add each column as a separate total and then combine. The end result is the same.

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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

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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SUBTRACTING WHOLE NUMBERS

3 Steps1. Align the minuend and

subtrahend by place values.

Check 70+60130

3. Moving to the left, repeat Step 2 until all place values in the subtrahend are subtracted.

Example 130 (Minuend)

- 60 (Subtrahend)

70 Difference

2. 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.

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2. Multiply the right digit of the multiplier with the right digit of the multiplicand. Keep multiplying as you move left through the multiplicand.

836

Example

418 (Multiplicand)

x 52 (Multiplier)

4 Steps1. Align the multiplicand and

multiplier at the right.

MULTIPLICATION OF WHOLE NUMBERS

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MULTIPLICATION OF WHOLE NUMBERS

3. Your partial product right digit or first digit is placed directly below the digit in the multiplier that you used to multiply.

2,090 (Partial Product)

4. Continue steps 2 and 3 until the multiplication process is complete. Add the partial products to get the final product.

21,736 (Product)

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CHECKING AND ESTIMATING MULTIPLICATION

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Check

52

x 418

416

52

20 8

21,736

Check the multiplication process by reversing the multiplicand and multiplier and then multiplying.

Estimate

50

x 400

20,000

MULTIPLICATION SHORTCUT WITH NUMBERS ENDING IN ZERO

1. When zeros are at the end of the multiplicand or the multiplier, or both, disregard the zeros and multiply.

3 Steps

2. Count the number of zeros in the multiplicand and multiplier. (4)

Example

65000 (3 zeros)

x 420 (1 zero)

(4 zeros)

3. Attach the number of zeros counted in Step 2 to your answer.

Solution

65 x 42 130 260 27,300,000

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MULTIPLYING A WHOLE NUMBER BY A POWER OF 10

99 x 10 99 x 100

99 x 1,000

1. Count the number of zeros in the power of 10.

2 Steps

2. Attach that number of zeros to the right side of the other whole number to obtain the answer. Insert commas as needed.

= 990 = 990 <----Add 1 Zero= 9,900 = 9,900 <----Add 2 Zero= 99,000 = 99,000 <----Add 3 Zero

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Divisor

Quotient

Dividend

DIVISION OF WHOLE NUMBERS

1

15

120

8

120 0

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

Example

15 270

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Example

7 169

DIVISION OF WHOLE NUMBERS

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

Divisor

Quotient

Dividend

2

14

29

4 R 1

28

1

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ESTIMATING AND CHECKING DIVISION

Check

138

x 36

828

4 14

4,968

+ 111

5,079

Estimate 50100 5,000

Example 36 R 111 Quotient

Divisor 138 5079 Dividend 414 939 828

111

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DIVISION SHORTCUT WITH NUMBERS

ENDING IN ZEROS2 Steps

= 9,500 <----Drop 1 Zero= 950 <----Drop 2 Zeros= 95 <----Drop 3 Zeros

2. Drop the same number of zeros in the dividend as in the divisor, counting from right to left.

95,000 / 10 -- 95,000 95,000 / 100 -- 95,000

95,000 / 1,000 -- 95,000

1. Count the number of ending zeros in the divisor.

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