Chapter 1 Whole Numbers How to Dissect and

#1 Whole Numbers; How to Dissect and Solve Word Problems Learning Unit Objectives LU 1. 1 Reading, Writing, and Rounding Whole Numbers 1. 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 Mc. Graw-Hill/Irwin 1 -2 solving a word problem © 2011 The Mc. Graw-Hill Companies, All Rights Reserved

#1 Whole Numbers; How to Dissect and Solve Word Problems Learning Unit Objectives LU 1. 2 Adding and Subtracting Whole Numbers 1. Add whole numbers; check and estimate addition computations 2. Subtract whole numbers; check and estimate subtraction computations Mc. Graw-Hill/Irwin 1 -3 © 2011 The Mc. Graw-Hill Companies, All Rights Reserved

#1 Whole Numbers; How to Dissect and Solve Word Problems Learning Unit Objectives LU 1. 3 Multiplying and Dividing Whole Numbers 1. Multiply whole numbers; check and estimate multiplication computations 2. Divide whole numbers; check and estimate computations Mc. Graw-Hill/Irwin 1 -4 © 2011 The Mc. Graw-Hill Companies, All Rights Reserved

1 -5 Hundred millions Ten millions 6 0 5 , 7 4 3 , 8 Tens 1 , 4 1 2 Decimal Point Thousands Ones Hundreds 9 Comma Figure 1. 1 Thousands Ten Thousands Millions Hundred Thousands Comma Billions 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

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 -6 8 9 , 4 1 2 Decimal Point 1 Ones , Tens 3 Hundreds 4 Comma 7 Units Thousands Ten millions , Ten Thousands Hundred millions 5 Hundred Thousands Comma 0 Comma Billions 6 Thousands Millions Ten billions 1 , Millions Hundred billions Billions Comma Trillions Ten trillions Hundred trillions Trillions

Converting parts to a regular whole number Convert 2. 3 billion to a regular whole number Step 1. Drop decimal point and insert a comma 2, 3 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 -7 2, 300, 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 -8 9400

Rounding all the way Step 1. Identify leftmost digit Step 3. Change all other digits to zero 7843 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 -9 8000

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 -10

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. 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 ------> $200, 000 Profit: Twenty-two million, five hundred fifty-six thousand dollars ----> $22, 556, 000 -----> $20, 000 1 -11

Adding Whole Numbers 3 Steps 1. Align the numbers according to their place values 1 -12 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

Estimate Addition by Rounding All the Way Example 211 1 -13 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.

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 -14 Example 13 130 (Minuend) - 60 (Subtrahend) 70 Difference Check 70 +60 130

Multiplication of Whole Numbers 4 Steps 1. Align the multiplicand 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 -15 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 multiplier and then multiplying 1 -16 416 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 multiplier. (4) 3. Attach the number of zeros counted in Step 2 to your answer 1 -17 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 <----Add 1 Zero 99 x 100 = 9, 900 <----Add 2 Zero 99 x 1, 000 = 99, 000 <----Add 3 Zero 1 -18

Division of Whole Numbers • How many times one number (Divisor) is contained in another number (Dividend). The result is the Quotient. 1 -19 Divisor Example 18 15 270 15 120 0 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 -20