Whole Numbers - Mackay Education

Chapter 1 Objectives Place Value Reading and Writing Whole Numbers Rounding Whole Numbers Addition with Carrying Addition of More Than Two Numbers Subtraction with Regrouping Regrouping with Zeros Multiplication with Carrying Division by One Digit Division with Remainders Division by Larger Numbers Whole Numbers Unit 1

Pages 7 29 Page 7 Place Value Whole numbers are made up of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, & 9. The number 44 has two digits. The number 23,060 has five digits. The value of each digit is different because of its position in the number.

Every The position has a place value. table on the next slide gives the names of the first ten places in our whole number system. _, _ _ _, _ _ _, _ _ _ one billions hundred millions ten millions one millions hundred thousands ten thousands one thousands hundreds tens ones

Page 7 Place Value (Contd) Page 7 Place Value Example Find the value of 5 in 85,406. Page 8 Place Value Group Work Use the number 985 to answer problems 1-3. Item one is done for you. 1.

9 is in the hundreds place. 9 has a value of 900. 2. 8 is in the _______ place. 8 has a value of ___. 3. 5 is in the _______ place. 5 has a value of ___. There are 1,760 yards a mile. Use this number to answer problems 4-5. 4. 1 is in the _______ place. 1 has a value of ___. 5.

7 is in the _______ place. 7 has a value of ___. Page 8 Reading & Writing Whole Numbers Commas make numbers easier to read. Counting from the right, there is a comma after every three places. Large At numbers are read in groups of three.

each comma we say the name of the group of digits that are set off by the comma. Pages 8 9 R & W Group Work Supply the missing words you need to read each number. 1. 2,043,000 two million, forty-three thousand. 2. 502 five _______ two. 3. 4,080 four _______, eighty. 4. 58,320 fifty-eight _______, three hundred twenty. Write words to show how to read each number

5. 3,800 _______________________ 6. 19,007,200 _______________________ Page 9 To Reading & Writing Whole Numbers write whole numbers from words, watch for places that must be held with zeros. Example: write three million, four hundred eight thousand, six hundred as a whole number. This number contains no ten thousands, no

tens, and no ones (or units). Hold these places with zeros. 3,408,600 Pages 9 10 R & W Group Work Write each of the following as a whole number. 7. Three hundred eight _______

8. Ninety thousand, twenty-four 9. Eight hundred four thousand, five hundred _______ 10. Sixty thousand, three hundred 11. Eleven million, two hundred seven thousand _______ _______

_______ Page 10 Rounding Whole Numbers Rounding makes numbers easier to use when you dont need exact values. To round a whole number: 1. Underline the digit in the place to which you want to round. 2. If the digit to the right of the underlined digit is 5 or more add 1 to the underlined digit.

3. If the digit to the right of the underlined digit is 4 or less, do not change the underlined digit. 4. Replace the digits to the right of the underlined digit with zeros. Pages 10 11 Rounding Examples Round 2,374 to the nearest hundred. Round 29,624 to the nearest thousand.

Pages 10 11 Rounding Group Work Round To the nearest ten: 38 542 295 To the nearest hundred:

each number: 863 59,848 4,082 To the nearest thousand: 6,174 39,723 3,279 Page 11 Addition with Carrying The answer to an addition problem is called the

sum or total. When the sum of the digits in a column is a twodigit number, carry the digit at the left to the next column to the left. To add more than two numbers, find the total for each column. Page 11 Addition Example 857 + 268 = 857

+ 268 Pages 12 13 Addition Group Work 1. 44 + 57 = 2. 15 + 88 = 3. 68 + 46 = 4. 341 + 59 =

5. 48 + 485 = Page 14 Addition of More Than Two Numbers Commutative property of addition = changing the order of addends does not change the sum 4+2=2+4 Associative property of addition = changing the grouping of addends does not change the sum (2 + 3) + 4 = 2 + (3 + 4) Page 14

Addition Example 43 + 44 + 19 = 12 + 84 + 57 = Pages 14 15 Addition Group Work 1. 17 + 88 + 53 = 2. 236 + 1,940 + 375 =

3. 318 + 9,907 + 24,063 = 4. 8,016 + 11,238 +127 = 5. Dons Music Shop sold 1,026 tapes in March, in April they sold 963 tapes, and in May they sold 1,372 tapes. What were the total sales for those three months? Page 16 Subtraction with Regrouping The

answer to a subtraction problem is called the difference. When the bottom number in any column is too large to subtract from the top number, you must regroup the top number. You may know this operation as renaming or borrowing. Example: 85 39 = Pages 16 17 Subtraction Group Work 1. 58 29 = 2.

811 243 = 3. 6,175 496 = 4. 4,236 1,448 = 5. 683 people signed up to go on a trip to Miami. 506 people actually went on the trip. How many people who signed up did not go? Page 18 Regrouping with Zeros

To regroup with zeros, look at the first digit in the top number that is not zero. Example: 904 356 = Pages 18 19 Subtraction Group Work 1. 801 236 = 2. 706 267 =

3. 4,000 1,256 = 4. 7,000 1,270 = 5. The town of Midvale wants to raise $850,000 to build a new health center. They have collected $473,260 so far. How much more money do they need? Page 20 Multiplication With Carrying The

answer to a multiplication problem is called the product. When you multiply two digits, the product is often a two-digit number. You must carry the left digit to the next number you a re multiplying. Then add the digit you carry to the next product. Example: 76 x 29 = Pages 20 21 Multiplication Group Work 1. 74 x 6 = 2.

778 x 63 = 3. 24 x 866 = 4. 48 x 30 = 5. Rodney makes $370 a week. There are 52 weeks in a year. How much does Rodney make in one year? Page 22 Division by One Digit The

answer to a division problem is called the quotient. To find a quotient, repeat the four steps listed below until you complete the problem. 1. Divide 2. Multiply 3. Subtract and compare 4. Bring down the next number.

Pages 22 23 Division Example 6 504 Long division = Writing every step out. Short division = writing out only the answer and the number you get by subtracting Page 23 Division Group Work 1. 3 141 2.

8 616 3. 3 237 4. 9 2,484 5. Three friends equally shared a raffle prize of $750. How much did each of them get? Page 24 Division with Remainders If

you do not get zero in the last subtraction step of a division problem, you will have a remainder. 4 387 Page 25 Division Group Work 1. 1,542 8 = 2. 3,845 6 = 3. 2,183 8 =

4. 2,277 5 = 5. To make a climbing toy for her children, Mary is sawing pieces of wood each 4 feet long from a piece that is 19 feet long. How many pieces can Mary cut from the long piece? Assuming no waste, what will be the length of the remaining piece? Page 26 Division by Larger Numbers To divide by two-digit and three-digit numbers, you must estimate how many times one number divides into another number. When you estimate,

you make a guess. 62 2,976 Page 27 Division Group Work 1. 1,616 22 = 2. 6,910 85 = 3. 1,412 39 = 4.

2,406 91 = 5. Last year the Melinos paid $7,440 in mortgage payments. There are 12 months in a year. How much did they pay each month?

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