Quản trị kinh doanh - Chapter one: Whole numbers: how to dissect and solve word problems

Chapter OneWhole numbers: How to Dissect and Solve word problems1-1Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinLU 1-1: Reading, Writing, and Rounding Whole NumbersUse place values to read and write numeric and verbal whole numbers.Round whole numbers to the indicated position.Use blueprint aid for dissecting and solving a word problem.LU 1-2: Adding and Subtracting Whole NumbersAdd whole numbers; check and estimate addition computations.Subtract whole numbers; check and estimate subtraction computations.LU 1-3: Multiplying and Dividing Whole NumbersMultiply whole numbers; check and estimate multiplication computations.Divide whole numbers; check and estimate computations.Learning unit objectives1-2Whole Number place-value chart1,605,743,891,412 displayed on the Whole Number Group Chart:1-3Writing numeric and verbal whole numbers1,605,743,891,412 verbalized:One trillion, six hundred five billion, seven hundred forty-three million, eight hundred ninety-one thousand, four hundred twelve1-4Converting parts to a regular whole numberConvert 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.2,31-5Rounding 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. 9362Step 2. Identify the digit to the right. 9362If 5 or more, increase the identified digit by 1, if less than 5 do not change. 94621-6Rounding all the wayStep 2. Identify the digit to the right. 7843 8000Step 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. 7843Step 1. Identify the left most digit. 7843 1-7How to Dissect and Solve a Word ProblemOrganization and persistence1-8General Problem-Solving ProcedureStep 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).1-9How to Dissect and Solve a Word ProblemSales: One hundred ninety-four million dollars. ----------->$194,000,000 -----------> $200,000,000Profit: Twenty-two million, five hundred fifty-six thousand dollars --------> $22,556,000 ---------> $20,000,000Tootsie 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.1-10Adding Whole Numbers3 Steps1. Align the numbers according to their place values.Example 1,362 5,913 8,924 6,59422,7933. 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.1-11Alternative 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 22,793 1,362 5,913 8,924 6,594Add each column as a separate total and then combine. The end result is the same.1-12Estimate Addition by Rounding All the WayExample 2 1 1 1,362 5,913 8,924 6,59422,793Example 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.1-13Subtracting Whole Numbers3 Steps1. Align the minuend and subtrahend by place values.Check 70+601303. Moving to the left, repeat Step 2 until all place values in the subtrahend are subtracted.Example 130 (Minuend) - 60 (Subtrahend) 70 Difference2. 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. 1-142. Multiply the right digit of the multiplier with the right digit of the multiplicand. Keep multiplying as you move left through the multiplicand. 836Example 418 (Multiplicand) x 52 (Multiplier)4 Steps1. Align the multiplicand and multiplier at the right.Multiplication of Whole Numbers1-15Multiplication of Whole Numbers3. 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) 1-16Checking and Estimating Multiplication1-17Check 52 x 418 416 52 20 8 21,736Check the multiplication process by reversing the multiplicand and multiplier and then multiplying.Estimate 50 x 400 20,000 Multiplication Shortcut with Numbers Ending in Zero1. When zeros are at the end of the multiplicand or the multiplier, or both, disregard the zeros and multiply.3 Steps2. 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 27,300,0001-18Multiplying a Whole Number by a Power of 1099 x 10 99 x 10099 x 1,0001. Count the number of zeros in the power of 10.2 Steps2. 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 Zero1-19 DivisorQuotientDividendDivision of Whole Numbers11512081200Count how many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient.Example 15 270 1-20Example 7 169 Division of Whole NumbersCount how many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient. DivisorQuotientDividend214294 R 12811-21Estimating and Checking DivisionCheck 138 x 36 828 4 14 4,968+ 1115,079Estimate 50100 5,000Example 36 R 111 QuotientDivisor 138 5079 Dividend 414 939 828 1111-22Division Shortcut with Numbers Ending in Zeros2 Steps= 9,500 <----Drop 1 Zero= 950 <----Drop 2 Zeros= 95 <----Drop 3 Zeros2. 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 -- 95,0001. Count the number of ending zeros in the divisor.1-23