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Whole numbers: How to Dissect and Solve word problems. Chapter One. Learning unit objectives. LU 1-1: Reading, Writing, and Rounding Whole Numbers Use place values to read and write numeric and verbal whole numbers. Round whole numbers to the indicated position. - PowerPoint PPT Presentation
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Chapter OneWHOLE NUMBERS: HOW TO DISSECT AND SOLVE
WORD PROBLEMS
1-1
LU 1-1: Reading, Writing, and Rounding Whole Numbers1. 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 Numbers6. Multiply whole numbers; check and estimate
multiplication computations.7. Divide whole numbers; check and estimate
computations.
LEARNING UNIT OBJECTIVES
1-2
WHOLE NUMBER PLACE-VALUE CHART
1-3
1,605,743,891,412 displayed on the Whole Number Group Chart:
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
1-4
CONVERTING PARTS TO A REGULAR WHOLE NUMBER
1-5
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
ROUNDING WHOLE NUMBERS
1-6
9400Step 3. Drop all digits to the right of the identified digit.
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
ROUNDING ALL THE WAY
1-7
Step 2. Identify the digit to the right. 7843
8000
Step 3. Change all other digits to zero.
If 5 or more, increase the identified digit by 1, if less than 5 do not change.
7843
Step 1. Identify the left most digit. 7843
HOW TO DISSECT AND SOLVE A WORD PROBLEMOrganization and persistence
1-8
GENERAL PROBLEM-SOLVING PROCEDURE
Step 1. State the problem(s).
1-9
Step 4. Evaluate results.
Step 3. Does the solution make sense?
Step 2. Decide on the best method(s) to solve the problem(s).
HOW TO DISSECT AND SOLVE A WORD PROBLEM
Sales: One hundred ninety-four million dollars. ----------->$194,000,000 -----------> $200,000,000Profit: Twenty-two million, five hundred fifty-six thousand dollars --------> $22,556,000 ---------> $20,000,000
1-10
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.
ADDING WHOLE NUMBERS
3 Steps1. Align the numbers according
to their place values.
Example
1,362
5,913
8,924
6,594
22,793
1-11
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.
ALTERNATIVE CHECK
Ones Column 2 + 3 + 4 + 4 13Tens Column 6 + 1 + 2 + 9 18Hundreds Column 3 + 9 + 9 + 5 26Thousands Column 1 + 5 + 8 + 6 20
1-12
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.
ESTIMATE ADDITION BY ROUNDING ALL THE WAY
Example 2 1 1 1,362 5,913 8,924 6,59422,793
1-13
Example
1,000 6,000 9,000 7,00023,000
*Final answer could have more than one non-zero since total is not rounded all the way.
SUBTRACTING WHOLE NUMBERS
3 Steps1. Align the minuend and
subtrahend by place values.
1-14
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.
2. Multiply the right digit of the multiplier with the right digit of the multiplicand. Keep multiplying as you move left through the multiplicand.
8361
Example
418 (Multiplicand)
x 52 (Multiplier)
4 Steps1. Align the multiplicand and
multiplier at the right.
MULTIPLICATION OF WHOLE NUMBERS
1-15
1 2 X 418
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.
2,0902 (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)
CHECKING AND ESTIMATING MULTIPLICATION
1-17
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
1-18
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)
Example65000 (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
MULTIPLYING A WHOLE NUMBER BY A POWER OF 10
1-19
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
Divisor
QuotientDividend
DIVISION OF WHOLE NUMBERS
1-20
1
15120
8
120 0
Count how many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient.
Example
15 270
Example
7 169
DIVISION OF WHOLE NUMBERS
1-21
Count how many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient.
Divisor
QuotientDividend
2
1429
4 R 1
281
ESTIMATING AND CHECKING DIVISION
Check 138 x 36 828 4 14 4,968+ 1115,079
Estimate 50100 5,000
1-22
Example 36 R 111 Quotient
Divisor 138 5079 Dividend 414 939 828
111
DIVISION SHORTCUT WITH NUMBERS
ENDING IN ZEROS2 Steps
1-23
= 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.
PROBLEM 1-53
Website: Average daily unique visitor:
1. Orbitz.com 1,527,0002. Mypoints.com 1,356,0003. Americangreetings.com 745,0004. Bizrate.com 503,0005. Half.com 397,000
1,527,000 1,356,000 745,000 503,000+ 397,000 4,528,000 visitors
Solution:5 4,528,000
45 28 25
30 30
905,600 average
1-24
PROBLEM 1-63
90 + 70 + 65 + 310 = 535 customers x $9 $ 4,815
Solution (a):
Solution (b):
$4,815 x 52 = $250,380
1-25
PROBLEM 1-65
$71,000 - 6,820 ($1,388 + $4,402 + $1,030)$64,180
Solution:
1-26
PROBLEM 1-69
$ 900 + 1,200 $2,100 - 614 ($350 + $44 + $160 + $60) $1,486
Solution:
1-27
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