Unit 1 Whole Numbers

2 PLACE VALUE The value of any digit depends on its place value Place value is based on multiples of 10 as follows: UNITSTENSHUNDREDSTHOUSANDS TEN THOUSANDS HUNDRED THOUSANDS MILLIONS 2, 5 3 7, 6 1 5

3 1,572.3 can be written in expanded form as: one thousand five hundred seventy-two and three tenths EXPANDED FORM Place value held by each digit can be emphasized by writing the number in expanded form The only time “and” should be used in expanded form is in place of a decimal

4 ROUNDING Used to make estimates Rounding Rules: Determine place value to which the number is to be rounded Look at the digit immediately to its right If digit to right is less than 5, replace that digit and all following digits with zeros If digit to right is 5 or more, add 1 to the digit in the place to which you are rounding. Replace all following digits with zeros

5 ROUNDING EXAMPLES Round 674 to the nearest ten 7 is in tens place value, so look at 4 Since 4 is less than 5, leave the 7 alone and replace the 4 with a zero Ans: 670 Round 68,753 to the nearest thousand 8 is in thousands place value, so look at 7 Since 7 is greater than 5, raise 8 to 9 and replace 7, 5, and 3 with zeros Ans: 69,000

6 ADDITION Align numbers to be added as shown; line up digits that hold the same place value –Add digits holding same place value, starting on right = –Continue adding from right to left 367 –Write 4 in units place value and carry the one

7 SUBTRACTION Align number to be subtracted under the other number as shown; line up digits that hold the same place value –Since 5 cannot be subtracted from 3, you need to borrow from 8 (making it 7) and add 10 to 3 (making it 13) 5837 – 654 –Start at the right and work left: 7 – 4 = 3 3 –Now, 13 – 5 = 8; 7 – 6 = 1; and 5 – 0 = 5 518

8 MULTIPLICATION Write numbers to be multiplied as shown; line up digits that hold the same place value 2153 × 345 –First, multiply by units digit (5) Write product, starting at units position and going from right to left –Multiply by tens digit (4) Write product, starting at tens position and going from right to left 8612 –Follow same procedure with hundreds digit (3) –Add to obtain final product

9 DIVISION Write division problem with divisor outside long division symbol and dividend within symbol 5 Multiply: 25 × 5 = 125; write this under Bring down the 6 6 Subtract: 135 – 125 =  25 = 4; write this above 6 4 Multiply: 25 × 4 = 100; write this under Subtract: 106 – 100 = 6; this is the remainder r 6 25 does not go into 1 or 13, but will divide into  25 = 5; write 5 above the 5 in number 1356 as shown 6

10 ORDER OF OPERATIONS All arithmetic expressions must be simplified using the following order of operations: 1. Parentheses 2. Multiplication and division from left to right 3. Addition and Subtraction from left to right Evaluate: (9 + 4) × 16 – 8  Do the operation in parentheses first = 13 × 16 – 8  Multiply next = 208 – 8  Subtract last = 200

11 ORDER OF OPERATIONS “PEMDAS” or “Please Excuse My Dear Aunt Sally” are other pneumonic ways to recall. 1. Parenthsis 2. Exponents 3. Multiply 4. Divide 5. Add 6. Subtract Worked left to right if all that is left in the problem

12 PRACTICE PROBLEMS 1. Round 2,147,359 to each of the following place values: 2. Write each of the following in expanded form: a. 23,956 b. 963, MILLIONS HUNDRED THOUSANDS HUNDREDS TENS

13 PRACTICE PROBLEMS (Cont) 3. Perform each of the following operations (round to the thousandth if necessary): a b c d – 1659 – 9896 e. 158 f g. h. × 47 × 584

14 PRACTICE PROBLEMS (Cont) 4. Evaluate each of the following: a. (5 + 1) × 3 + (2 + 4) b (4 – 2) c (4 – 3)(12 + 6)  9 d. 35 –

15 Solutions 1. Rounding 1. 2,000, ,100, ,147, ,147, ,147, Expanding 1. Twenty three thousand nine hundred fifty-six 2. Nine hundred sixty three thousand five hundred eighty two and forty-five hundredths

16 Solutions 3. Operations a b c d e f g h Operations a. 24 b. 13 c. 29 d. 31