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Lecture Practical business math procedures (11/e) - Chapter 1: Whole numbers: how to dissect and solve word problems. The learning objectives for this chapter include: Reading, writing, and rounding whole numbers; adding and subtracting whole numbers; multiplying and dividing whole numbers.
Whole numbers: How to Dissect and Solve word problems Chapter One 1-1 McGrawHill/Irwin Copyright © 2014 by The McGrawHill Companies, Inc. All rights reserved 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 Use blueprint aid for dissecting and solving a word problem LU 1-2: Adding and Subtracting Whole Numbers Add whole numbers; check and estimate addition computations Subtract whole numbers; check and estimate subtraction computations LU 1-3: Multiplying and Dividing Whole Numbers Multiply whole numbers; check and estimate multiplication computations Divide whole numbers; check and estimate computations 1-2 Whole Number place-value chart 1,605,743,891,412 displayed on the Whole Number Group Chart: 1-3 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 Convert 2.3 million to a regular whole number Step Drop the decimal point and insert a comma Step 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 2,3 2,300,000 1-5 Rounding Whole Numbers Step Identify the place value of the digit you want to round 9362 Step Identify the digit to the right 9362 If or more, increase the identified digit by 1, if less than not change 9462 Step Drop all digits to the right of the digit you want to round 9400 1-6 Rounding all the way Step Identify the left most digit Step Identify the digit to the right 7843 If or more, increase the leftmost digit by 1; if less than 5, not change Step Change all other digits to zero 7843 7843 8000 1-7 How to Dissect and Solve a Word Problem Organization and persistence 1-8 General Problem-Solving Procedure Step State the problem(s) Step Decide on the best method(s) to solve the problem(s) Step Does the solution make sense? Step Evaluate results 1-9 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 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 1-10 Adding Whole Numbers Steps Align the numbers according to their place values Example 1,362 5,913 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 8,924 6,594 22,793 Moving to the left, repeat Step until all place values are added 1-11 Alternative check Add each column as a separate total and then combine The end result is the same Ones Column 2+3+4+4 Tens Column 6+1+2+9 Hundreds Column 3+9+9+5 Thousands Column 1+5+8+6 1,362 5,913 8,924 6,594 13 18 26 20 22,793 1-12 Estimate Addition by Rounding All the Way Example 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 non-zero since total is not rounded all the way 1-13 Subtracting Whole Numbers Steps Align the minuend and subtrahend by place values 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 from the tens digit in the minuend Moving to the left, repeat Step until all place values in the subtrahend are subtracted Example 130 (Minuend) - 60 (Subtrahend) 70 Difference Check 70 +60 130 1-14 Multiplication of Whole Numbers Steps Align the multiplicand and multiplier at the right Example 418 (Multiplicand) x 52 (Multiplier) Multiply the right digit of the multiplier with the right digit of the multiplicand Keep multiplying as you move left through the multiplicand 836 1-15 Multiplication of Whole Numbers Your partial product right digit or first digit is placed directly below the digit in the multiplier that you used to multiply Continue steps and until the multiplication process is complete Add the partial products to get the final product 2,090 (Partial Product) 21,736 (Product) 1-16 Checking and Estimating Multiplication Check Check the multiplication process by reversing the multiplicand and multiplier and then multiplying 52 x 418 416 52 20 Estimate 50 x 400 20,000 21,736 1-17 Multiplication Shortcut with Numbers Ending in Zero Example Steps 65000 (3 zeros) x 420 (1 zero) When zeros are at the end of the multiplicand or the multiplier, or both, disregard the zeros and multiply Count the number of zeros in the multiplicand and multiplier (4) (4 zeros) Solution 65 x 42 130 260 27,300,000 Attach the number of zeros counted in Step to your answer 1-18 Multiplying a Whole Number by a Power of 10 Steps Count the number of zeros in the power of 10 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 99 x 100 99 x 1,000 = 990 = 990 < Add Zero = 9,900 = 9,900 < Add Zero = 99,000 = 99,000 < Add Zero 1-19 Division of Whole Numbers Count how many times one number (Divisor) is contained in another number (Dividend) The result is the Quotient Example 18 Divisor Quotient Dividend 15 270 15 120 120 1-20 ... 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 Use blueprint aid for dissecting... results 1-9 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... 1-3 : Multiplying and Dividing Whole Numbers Multiply whole numbers; check and estimate multiplication computations Divide whole numbers; check and estimate computations 1-2 Whole Number place-value