Chapter 1 Whole Numbers © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 1.2 Adding Whole Numbers Objectives 1. Add two single-digit numbers. 2. Add more than two numbers. 3. Add when regrouping (carrying) is not required. 4. Add with regrouping (carrying). 5. Use addition to solve application problems. 6. Check the answers in addition. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 1 Adding Two Single-Digit Numbers Add, and then change the order of numbers to write another addition problem. 7 + 6 = 13 and 6 + 7 = 13 b. 9 + 6 = 15 and 6 + 9 = 15 c. 3 + 7 = 10 and 7 + 3 = 10 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. The sum of 6 + 7 + 8 may be found as follows. (6 + 7) + 8 = 13 + 8 = 21 Another way to add the same numbers is 6 + (7 + 8) = 6 + 15 = 21 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 2 Adding More Than Two Numbers Add 3, 4, 6, 2, and 5. 3 4 6 2 + 5 3 + 4 = 7 7 + 6 = 13 13 + 2 = 15 5 + 15 = 20 20 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 3 Adding without Regrouping Add 411 + 13 + 124 + 11. 4 1 1 1 3 1 2 4 + 1 1 Hundreds, tens and ones in a column 5 5 9 Sum of ones Sum of tens Sum of hundreds Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 4 Adding with Regrouping Add 48 and 36. 4 8 + 3 6 1 8 4 8 ones and 6 ones = 14 ones Regroup 14 ones as 1 ten and 4 ones. Write 4 ones in the ones column and write 1 ten in the tens column. Add the digits in the tens column, including the regrouped 1. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 5 Adding with Regrouping (Carrying) Add 226 + 7756 + 24 + 8 + 85. 2 2 6 7 7 5 6 2 4 8 + 8 5 1 1 2 Sum the ones column (29). Write 9 in the ones column and write 2 in the tens column. Sum the tens column (19). Write 9 in the tens column and write 1 in the hundreds column. Sum the hundreds column, including the regrouped 1. 8 9 9 Sum the thousands column, including the regrouped 1. The sum is 8099. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 6 Applying Addition Skills On this map of the Walt Disney World area in Florida, the distance in miles from one location to another is written alongside of the road. Find the shortest route from Orlando to Belle Isle. Solution Add the mileage along various routes to determine the distances from Orlando to Belle Isle. Orlando to Resort 9 Resort to Pine 6 Pine to Belle _3_ 18 miles Copyright © 2010 Pearson Education, Inc. All rights reserved.

Applying Addition Skills Parallel Example 6 Applying Addition Skills On this map of the Walt Disney World area in Florida, the distance in miles from one location to another is written alongside of the road. Find the shortest route from Orlando to Belle Isle. Solution Another possible route: Orlando to Clear Lake 9 Clear Lake to Shadow 6 Shadow to Conway 3 Conway to Belle _6_ 24 miles The shortest route is from Orlando to Resort Area to Pine Castle to Belle Island, 18 miles Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 7 Finding a Total Distance Use the map to find the total distance from Bertha to Clear Lake to Shadow Hills and back to Bertha. Solution Add the mileage from Bertha to Clear Lake to Shadow Hills to Bertha. Bertha to Winter Park 7 Winter Park to Clear Lake 7 Clear Lake to Shadow Hills 11 Shadow Hills to Bertha 9_ 34 miles Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 8 Finding a Perimeter Find the number of feet of fencing needed enclose the farm pasture shown. Solution 1575 ft Find the perimeter, or total distance around the pasture by adding the lengths of all the sides. 375 ft 375 ft 1575 375 + 375 1575 ft 3900 miles The amount of fencing needed is 3900 ft. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 9 Checking Addition Check the following addition. 4 4 8 2 4 6 + 7 2 7 6 6 Add down. 7 6 6 To check, add up. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Chapter 1 Whole Numbers © 2010 Pearson Education, Inc. All rights reserved.

1.3 Subtracting Whole Numbers Objectives 1. Change addition problems to subtraction and subtraction problems to addition. 2. Identify the minuend, subtrahend, and difference. 3. Subtract when no regrouping (borrowing) is needed. 4. Check subtraction answers by adding. 5. Subtract with regrouping (borrowing). 6. Solve application problems with subtraction. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 16

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 1 Changing Addition Problems to Subtraction Change the addition problem 6 + 2 = 8 to a subtraction problem. Two subtraction problems are possible. 8 – 2 = 6 or 8 – 6 = 2 8 – 2 = 6 8 – 6 = 2 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 17

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 2 Changing Subtraction Problems to Addition Change each subtraction problem to an addition problem. 9 – 4 = 5 9 = 4 + 5 It is also correct to write 9 = 5 + 4. 21 – 8 = 13 21 = 8 + 13 or 21 = 13 + 8 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 18

Copyright © 2010 Pearson Education, Inc. All rights reserved. In subtraction, as in addition, the numbers in a problem have names. 12 – 8 = 4 12 is the minuend 8 is the subtrahend 4 is the difference or answer 12 – 8 = 4 Difference Minuend Subtrahend Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 19

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 3 Subtracting Two Numbers Subtract. 8 7 4 – 2 4 1 Digits are lined up. Subtract from right to left. 6 3 3 7 tens – 4 tens 4 ones – 1 one 8 hundreds – 2 hundreds Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 20

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 4 Checking Subtraction by Using Addition Use addition to check the answer. If the answer is incorrect find the correct answer. 3 5 6 – 1 2 3 2 3 3 Match Rewrite as an addition problem. 233 + 123 356 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 21

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 5 Subtracting with Regrouping Subtract 28 from 72. 7 2 – 2 8 6 12 2 is less than 8, so we must regroup 1 ten as 10 ones. 7 tens – 1 ten = 6 tens 4 4 Now subtract 8 ones from 12 ones in the ones column. Then subtract 2 tens from 6 tens in the tens column. You can check by adding 44 and 28; you should get 72. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 22

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 6 Subtracting with Regrouping Subtract by regrouping when necessary. a. 6 9 5 3 – 2 4 5 4 13 6 7 8 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 23

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 6 Subtracting with Regrouping Subtract by regrouping when necessary. b. 7 3 2 – 4 5 3 12 6 2 12 2 7 9 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 24

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 7 Regrouping with Zeros Subtract. 5 7 0 8 – 2 1 7 9 9 6 10 18 3 5 2 9 There are no tens that can be regrouped into ones. So you must first regroup 1 hundred as 10 tens. Now we may regroup from the tens position. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 25

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 8 Regrouping with Zeros Subtract. 8 0 0 0 – 2 9 9 9 9 9 7 10 10 10 5 1 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 26

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 10 Applying Subtraction Skills Use the table to find how much more, on average, a person with a Professional degree earns each year than a person with a Bachelor’s degree. Solution Find the average earnings of each type of degree and subtract. Professional $118,785 Bachelor’s $ 56,655 $62,130 more earnings Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.3- 27

Chapter 1 Whole Numbers © 2010 Pearson Education, Inc. All rights reserved.

1.7 Rounding Whole Numbers Objectives 1. Locate the place to which a number is to be rounded. 2. Round numbers. 3. Round numbers to estimate an answer. 4. Use front end rounding to estimate an answer. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 29

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 30

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 2 Using Rounding Rules for 4 or Less Round 643 to the nearest hundred. Step 1 Step 2 Step 3 Locate the place to which the number is being rounded. Draw a line under that place. 643 Because the next digit to the right of the underlined place is 4, which is 4 or less, do not change the digit in the underlined place. Next digit is 4 or less. 643 6 remains 6. Change all digits to the right of the underlined place to zeros. 643 rounded to the nearest hundred is 600. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 31

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 3 Using Rounding Rules for 5 or More Round 27,621 to the nearest thousand. Step 1 Step 2 Step 3 Locate the place to which the number is being rounded. Draw a line under that place. 27,621 Because the next digit to the right of the underlined place is 6, which is 5 or more, add 1 to the underlined place. Next digit is 5 or more. 27,621 Change 7 to 8. Change all digits to the right of the underlined place to zeros. 27,621 rounded to the nearest thousand is 28,000. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 32

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 4 Using Rounding Rules a. Round 2271 to the nearest ten. Step 1 Step 2 Step 3 2271 The next digit to the right is 1, which is 4 or less. Next digit is 4 or less. 2271 Leave 7 as 7. Change to 0. 2270 2271 is closer to 2270 than to 2280. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 33

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 4 Using Rounding Rules b. Round 14,972 to the nearest hundred. Step 1 Step 2 Step 3 14,972 The next digit to the right is 7. Next digit is 5 or more. 14,972 Change 9 to 10; write 0 and regroup 1 into thousands place. Change to 0. 15,072 14,972 is closer to 15,000 than to 14,000. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 34

Rounding Large Numbers Parallel Example 5 Rounding Large Numbers Round 48,751 to the nearest ten-thousand. Step 1 Step 2 Step 3 48,751 The next digit to the right is 8. Next digit is 5 or more. 48,751 Change 4 to 5. 58,751 Change to 0. 48,751 rounded to the nearest ten-thousand is 50,000. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 35

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 6 Rounding to Different Places Round 736 to the (a) nearest ten and (b) the nearest hundred. nearest ten b. nearest hundred Next digit is 5 or more. 736 Tens place (3 + 1 = 4) 736 rounded to the nearest ten is 740. Next digit is 4 or less. 736 Hundreds place stays the same. 736 rounded to the nearest hundred is 700. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 36

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 8 Using Rounding to Estimate an Answer Estimate each answer by rounding to the nearest ten. a. 28 30 41 40 Rounded to the nearest ten 91 90 + 46 + 50 210 Estimated answer Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 37

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 8 Using Rounding to Estimate an Answer Estimate each answer by rounding to the nearest ten. b. 65 70 Rounded to the nearest ten 38 – 40 – 30 Estimated answer Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 38

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 8 Using Rounding to Estimate an Answer Estimate each answer by rounding to the nearest ten. c. 72 70 Rounded to the nearest ten 46 x 50 x 3500 Estimated answer Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 39

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 9 Using Rounding to Estimate an Answer Estimate each answer by rounding to the nearest hundred. a. 723 700 285 300 Rounded to the nearest hundred 197 200 + 644 + 600 1800 Estimated answer Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 40

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 9 Using Rounding to Estimate an Answer Estimate each answer by rounding to the nearest hundred. b. 832 800 Rounded to the nearest hundred – 274 – 300 500 Estimated answer Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 41

Copyright © 2010 Pearson Education, Inc. All rights reserved. A convenient way to estimate an answer is to use front end rounding. With front end rounding, we round to the highest possible place so that all digits become 0 except for the first one. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 42

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 10 Using Front End Rounding to Estimate an Answer Estimate each answer using front end rounding. a. 38 40 All digits changed to 0 except first digit, which is rounded 1624 2000 4178 4000 + 339 + 300 6340 Estimated answer Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 43

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 10 Using Front End Rounding to Estimate an Answer Estimate each answer using front end rounding. b. 5162 5000 First digit rounded and all others changed to 0. – 875 – 900 4100 Estimated answer Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 44

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 10 Using Front End Rounding to Estimate an Answer Estimate each answer using front end rounding. c. 8250 8000 First digit rounded and all others changed to 0. x 36 x 40 320,000 Estimated answer Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.7- 45

Chapter 1 Whole Numbers © 2010 Pearson Education, Inc. All rights reserved.

1.4 Multiplying Whole Numbers Objectives 1. Identify the parts of a multiplication problem. 2. Do chain multiplication. 3. Multiply by single-digit numbers. 4. Use multiplication shortcuts for numbers ending in zero. 5. Multiply by numbers having more than one digit. 6. Solve application problems with multiplication. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 47

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 48

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 1 Multiplying Two Numbers Multiply. a. 4 × 7 = b. 8 ∙ 0 = c. 7(6) = 28 42 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 49

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 50

Multiplying Three Numbers Parallel Example 2 Multiplying Three Numbers Multiply 5 × 4 × 3. (5 × 4) × 3 20 × 3 = 60 Also, 5 × (4 × 3) 5 × 12 = 60 Either grouping results in the same product. Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1.4- 51

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 3 Multiplying with Regrouping Multiply. 6 2 7 × 4 1 2 2 5 8 4 × 7 = 28 ones, write 8 ones; write 2 tens in the tens column. 4 × 2 = 8 tens, add the 2 regrouped tens to get 10 tens. Write 0 tens and 1 hundred in the hundreds column. 4 × 6 hundreds = 24 hundreds; add the1 regrouped hundred to get 25 hundreds. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 52

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 4 Using Multiples of 10 to Multiply Multiply. a. 29 × 10 = b. 53 × 100 = c. 409 × 1000 = 290 Attach 0. 5300 Attach 00. 409,000 Attach 000. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 53

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 5 Using Multiples of 10 to Multiply Multiply. 25 × 5000 Multiply 25 by 5, then attach the three zeros. 25 × 5 125 25 × 5000 = 125,000 Attach 000. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 54

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 6 Multiplying with More Than One Digit Multiply 58 and 24. First multiply 58 by 4. 3 Regrouping is needed here. 58 × 4 232 Now multiply 58 by 20. 58 × 20 1160 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 55

Multiplying with More Than One Digit Parallel Example 6 continued Multiplying with More Than One Digit Multiply 58 and 24. Add the results. 58 × 24 232 + 1160 58 × 4 58 × 20 1392 Add. Both 232 and 1160 are called partial products. To save time, the 0 in the 1160 is usually not written. Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1.4- 56

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 7 Using Partial Products Multiply. 3 4 4 × 1 2 1 6 8 8 Tens lined up. Hundreds lined up. 4 1, 6 2 4 Product Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 57

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 8 Multiplying with Zeros Multiply. 5 2 9 × 4 0 2 1 0 5 8 0 0 0 2 1 1 6 Tens lined up. Hundreds lined up. 2 1 2, 6 5 8 Product Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 58

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 9 Applying Multiplication Skills Find the cost of 27 lamps priced at $92 each. Approach Multiply the number of lamps (27) by the cost of one lamp ($92). Solution 2 7 × 9 2 5 4 2 4 3 2 4 8 4 The total cost of the lamps is $2484. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.4- 59

Chapter 1 Whole Numbers © 2010 Pearson Education, Inc. All rights reserved.

1.8 Exponents, Roots, and Order of Operations Objectives 1. Identify an exponent and a base. 2. Find the square root of a number. 3. Use the order of operations. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.8- 61

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 1 Simplifying Expressions Identify the exponent and the base and then simplify each expression. a. 35 Exponent Base 35 35 = 3 × 3 × 3 × 3 × 3 = 243 b. 73 73 = 7 × 7 × 7 = 343 The base is 7 and the exponent is 3. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.8- 62

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.8- 63

Copyright © 2010 Pearson Education, Inc. All rights reserved. Parallel Example 2 Using Perfect Squares Find each square root. a. b. c. = 8 = 11 = 14 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.8- 64

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 1.8- 65