Kinh tế học - Chapter 1: Whole numbers: how to dissect and solve problems

Chapter 1Whole Numbers: How to Dissect and Solve ProblemsUse place values to read and write numeric and verbal whole numbersRound whole numbers to the indicated positionUse blueprint aid for dissecting and solving a word problemWhole Numbers; How to Dissect and Solve Word Problems#1Learning Unit ObjectivesReading, Writing, and Rounding Whole NumbersLU1.11-2Add whole numbers; check and estimate addition computationsSubtract whole numbers; check and estimate subtraction computationsWhole Numbers; How to Dissect and Solve Word Problems#1Learning Unit ObjectivesAdding and Subtracting Whole NumbersLU1.21-3Multiply whole numbers; check and estimate multiplication computationsDivide whole numbers; check and estimate computationsWhole Numbers; How to Dissect and Solve Word Problems#1Learning Unit ObjectivesMultiplying and Dividing Whole NumbersLU1.31-4Figure 1.1Whole-number place-value chartHundred billionsHundred trillionsTen ThousandsHundred ThousandsThousandsHundredsCommaTen trillionsTrillionsTen billionsBillionsCommaHundred millionsTen millionsMillionsCommaCommaTensOnes 1 , 6 0 5 , 7 4 3 , 8 9 1 , 4 1 2 1,605,743,891,412Decimal PointTrillionsBillionsMillionsUnitsThousandsWriting numeric and verbal whole numbersHundred billionsHundred trillionsTen ThousandsHundred ThousandsThousandsHundredsCommaTen trillionsTrillionsTen billionsBillionsCommaHundred millionsTen millionsMillionsCommaCommaTensOnes 1 , 6 0 5 , 7 4 3 , 8 9 1 , 4 1 2 One trillion, six hundred five billion, seven hundred forty three million, eight hundred ninety one thousand, four hundred twelveDecimal PointTrillionsBillionsMillionsUnitsThousandsConverting parts to a regular whole number2,3Convert 2.3 billion to a regular whole numberStep 2. Add zeros so the leftmost digit ends in the word name of the amount youwant to convert. Be sure to add commasas needed.Step 1. Drop decimal point and insert a comma2,300,000,000Rounding Whole Numbers93629462Step 1. Identify the place value of the digit you want to roundStep 2. Identify the digit to the right.If 5 or more, increase the identified digitby 1, if less than 5 do not changeStep 3. Drop all digits to the rightof the identified digit9400Rounding all the way78437843Step 1. Identify leftmost digitStep 2. Identify the digit to the right.If 5 or more, increase the identified digitby 1, if less than 5 do not changeStep 3. Change all other digits tozero8000General Problem-Solving ProcedureStep 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 resultsHow to Dissect and Solve a Word ProblemTootsie 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.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 -----------> $200,000,000Profit: Twenty-two million, five hundred fifty-six thousand dollars --------> $22,556,000 ---------> $20,000,000Adding Whole Numbers3 Steps1. Align the numbers according to their place values2. 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.3. Moving to the left, repeat Step 2 until all place values are added.Example 2 1 1 1,362 5,913 8,924 6,59422,793Estimate Addition by Rounding All the WayExample 2 1 1 1,362 5,913 8,924 6,59422,793Example 211 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 Numbers3 Steps1. Align the minuend and subtrahend by place values2. 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 subtractedExample 13 130 (Minuend) - 60 (Subtrahend) 70 DifferenceCheck 70+60 130Multiplication of Whole Numbers4 Steps1. 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.Example 418 (Multiplicand) x 52 (Multiplier) 83620 90 (Partial Product) 21,736 (Product) Checking and Estimating MultiplicationCheck 52 x 418 416 52 20 821,736Estimate 50 x 400 20,000 Check the multiplication process by reversing the multiplicand and multiplier and then multiplyingMultiplication Shortcut with Numbers Ending in Zero3 Steps1. When zeros are at the end of the multiplicand or the multiplier, or both, disregard the zeros and multiply2. Count the number of zeros in the multiplicand and multiplier. (4)3. Attach the number of zeros counted in Step 2 to your answerSolution 65 x 42 130 260 27,300,000Example65000 (3 zeros)x 420 (1 zeros)(4 zeros)Multiplying a Whole Number by a Power of 102 StepsCount 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 Zero99 x 100 = 9,900 = 9,900 <----Add 2 Zero99 x 1,000 = 99,000 = 99,000 <----Add 3 ZeroDivision of Whole NumbersHow many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient.Example 18 Quotient Divisor 15 270 Dividend 15 120 120 0Division Shortcut with Numbers Ending in Zeros2 Steps1. 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 Zero95,000 / 100 -- 95,000 = 950 <----Drop 2 Zeros95,000 / 1,000 -- 95,000 = 95 <----Drop 3 Zeros