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Whole Numbers; How to Dissect and Solve Word Problems Kirkwood Community College January 26, 2009 Presented by Sanh Tran, MBA, CPIM, CTL 1-1 Chapter 1 Whole Numbers: How to Dissect and Solve Problems McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved #1 Whole Numbers; How to Dissect and Solve Word Problems Learning Unit Objectives LU1.1 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 • Use blueprint aid for dissecting and McGraw-Hill/Irwin 1-3 solving a word problem ©2008 The McGraw-Hill Companies, All Rights Reserved #1 Whole Numbers; How to Dissect and Solve Word Problems Learning Unit Objectives LU1.2 Adding and Subtracting Whole Numbers • Add whole numbers; check and estimate addition computations • Subtract whole numbers; check and estimate subtraction computations McGraw-Hill/Irwin 1-4 ©2008 The McGraw-Hill Companies, All Rights Reserved #1 Whole Numbers; How to Dissect and Solve Word Problems Learning Unit Objectives LU1.3 Multiplying and Dividing Whole Numbers • Multiply whole numbers; check and estimate multiplication computations • Divide whole numbers; check and estimate computations McGraw-Hill/Irwin 1-5 ©2008 The McGraw-Hill Companies, All Rights Reserved 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 1-6 1-7 Comma Hundred millions 6 0 5 , 7 3 , 8 9 1 , 4 Ones Tens Thousands Hundreds Comma Figure 1.1 Thousands Ten Thousands Millions Hundred Thousands Comma 4 Millions Billions Ten millions Billions 1 , Ten billions Trillions Hundred billions Comma Trillions Ten trillions Hundred trillions Whole-number place-value chart 1,605,743,891,412 Units 1 2 Writing numeric and verbal whole numbers One trillion, six hundred five billion, seven hundred forty three million, eight hundred ninety one thousand, four hundred twelve 1-8 8 9 , 4 Ones 1 Tens , Hundreds 3 Comma 4 Units Thousands 7 Ten Thousands , Hundred Thousands Hundred millions 5 Comma Comma 0 Thousands Millions Billions 6 Ten millions Ten billions 1 , Millions Hundred billions Billions Comma Trillions Ten trillions Hundred trillions Trillions 1 2 Converting parts to a regular whole number Convert 2.4 billion to a regular whole number Step 1. Drop decimal point and insert a comma 2,4 Step 2. Add zeros so the leftmost digit ends in the word name of the amount you want to convert. Be sure to add commas as needed. 1-9 2,400,000,000 Rounding Whole Numbers Step 1. Identify the place value of the digit you want to round 9362 Step 3. Drop all digits to the right of the identified digit 9462 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 1-10 9400 Rounding all the way Step 1. Identify leftmost digit Step 3. Change all other digits to zero 9362 9362 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 1-11 9000 How to Dissect and Solve a Word Problem Organization and persistence The Facts Solving for? Steps to take Key Points 1-12 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 1-13 How to Dissect and Solve a Word Problem Tootsie Roll Industries sales reached one hundred ninetyfour 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 Points Sales: 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 1-14 Addition • Addends: Numbers that are to be added together in an addition. • Sum (Amount or total): The result of an addition. 1-15 Adding Whole Numbers 3 Steps 1. Align the numbers according to their place values 1-16 Example 211 1,362 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. 5,913 3. Moving to the left, repeat Step 2 until all place values are added. 22,793 8,924 6,594 Alternative check 1,362 Add each column as a separate total and then combine. The end result is the same. 5,913 8,924 6,594 13 18 26 20 22,793 1-17 Estimate Addition by Rounding All the Way Example 211 1-18 Example 211 1,362 1,000 5,913 6,000 8,924 9,000 6,594 7,000 22,793 23,000 *Final answer could have more than one nonzero since total is not rounded all the way. 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. 1-19 Subtracting Whole Numbers 3 Steps 1. Align the minuend and subtrahend by place values 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. 3. Moving to the left, repeat Step 2 until all place values in the subtrahend are subtracted 1-20 Example 12 3 2 12 4,327 (Minuend) -1,340 (Subtrahend) 2,987 Difference Check 2,987 +1,340 4,327 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. 1-21 Multiplication of Whole Numbers 4 Steps 1. 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. 1-22 Example 418 (Multiplicand) x 52 (Multiplier) 836 20 90 (Partial Product) 21,736 (Product) Checking and Estimating Multiplication Check 52 x 418 Check the multiplication process by reversing the multiplicand and multiplier and then multiplying 1-23 416 52 20 8 21,736 Estimate 50 x 400 20,000 Multiplication Shortcut with Numbers Ending in Zero Example 3 Steps 1. 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) 3. Attach the number of zeros counted in Step 2 to your answer 1-24 65000 (3 zeros) x 420 (1 zeros) (4 zeros) Solution 65 x 42 130 260 27,300,000 Multiplying a Whole Number by a Power of 10 2 Steps 1. 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 Zero 99 x 100 = 9,900 = 9,900 <----Add 2 Zero 99 x 1,000 = 99,000 = 99,000 <----Add 3 Zero 1-25 Division • Dividend: The number that will be divided by another • • • • 1-26 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. Division of Whole Numbers • How many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient. 1-27 Divisor Example 18 15 270 15 120 120 0 Quotient Dividend Division of Whole Numbers • How many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient. 1-28 Divisor Example 36 R 111 138 5,079 4 14 939 828 111 Quotient Dividend Estimating and Checking Division Check 138 x 36 828 4 14 4,968 + 111 5,079 1-29 Divisor Example 36 R 111 138 5,079 4 14 939 828 111 Estimate 50 100 5,000 Quotient Dividend 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 Zero 95,000 / 100 -- 95,000 = 950 <----Drop 2 Zeros 95,000 / 1,000 -- 95,000 = 95 <----Drop 3 Zeros 1-30 Problem 1-40 Solution: 42 R18 46 1,950 Check: 184 46 x 42 = 1,932 110 + 18 (R) 92 1,950 18 1-31 Problem 1-53 Website: 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 Solution: 1,527,000 1,356,000 745,0000 503,000 + 397,000 4,528,000 visitors 1-32 Average daily unique visitor: 905,600 average 5 4,528,000 45 28 25 30 30 Problem 1-54: Solution: 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 1-33 Problem 1-56 • 90, 65, 85, 80, 75 and 90 • • • • 1-34 ↓ Lowest grade: 65 90+85+80+75+90 = 420 5 different grades 420÷5 = 84 (average grade) Problem 1-63: Solution (a): Total customers in the week: 90 + 70 + 65 + 310 = 535 customers Total sales for the week: 535 x $9 $4,815 Solution (b): 52 weeks in a year Total sales for the year: 1-35 $4,815 x 52 = $250,380 Problem 1-65: Solution: 1.Calculate the total deductions: $1,462 + $3,782 + $884 = 6,128 2. Calculate net pay: $61,000 - 6,128 _______ $54,872 1-36 Problem 1-69: Expenses: Solution: $350 + $44 + $160 + $60=614 Deposit: 1,200 $ 900 + 1,200 $2,100 (Subtotal after deposit) - 614 (Less subtotal for expenses) $1,486 1-37 Reference • Slater, J. (2008). Practical business math procedures (9th ed.). New York: McGrawHill/Irwin 1-38 Homework (5 points total) 1-39 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)