Chapter One WHOLE NUMBERS: HOW TO DISSECT AND SOLVE WORD PROBLEMS 1-1 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin
Dec 18, 2015
Chapter OneWHOLE NUMBERS: HOW TO DISSECT AND SOLVE
WORD PROBLEMS
1-1
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
1-5
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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