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Unit 1

Unit 1. Whole Numbers. PLACE VALUE. The value of any digit depends on its place value Place value is based on multiples of 10 as follows:. HUNDRED THOUSANDS. TEN THOUSANDS. MILLIONS. THOUSANDS. HUNDREDS. TENS. UNITS. 2 , 5 3 7 , 6 1 5.

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Unit 1

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  1. 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: HUNDRED THOUSANDS TEN THOUSANDS MILLIONS THOUSANDS HUNDREDS TENS UNITS 2 , 5 3 7 , 6 1 5

  3. 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 1,572.3 can be written in expanded form as: one thousand five hundred seventy-two and three tenths

  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 1 • Add digits holding same place value, starting on right • 8 + 6 = 14 1538 + 2136 367 • Write 4 in units place value and carry the one 4 • Continue adding from right to left

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

  8. MULTIPLICATION • Write numbers to be multiplied as shown; line up digits that hold the same place value • First, multiply by units digit (5) Write product, starting at units position and going from right to left 2153 × 345 • Multiply by tens digit (4) Write product, starting at tens position and going from right to left 10765 8612 6459 • Follow same procedure with hundreds digit (3) 742785 • Add to obtain final product

  9. DIVISION • Write division problem with divisor outside long division symbol and dividend within symbol • 25 does not go into 1 or 13, but will divide into 135. 135  25 = 5; write 5 above the 5 in number 1356 as shown 5 4 r 6 125 • Multiply: 25 × 5 = 125; write this under 135 10 6 • Subtract: 135 – 125 = 10 100 • Bring down the 6 • 106  25 = 4; write this above 6 6 • Multiply: 25 × 4 = 100; write this under 106 • Subtract: 106 – 100 = 6; this is the remainder

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

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

  12. PRACTICE PROBLEMS • Round 2,147,359 to each of the following place values: • Write each of the following in expanded form: a. 23,956 b. 963,582.45

  13. PRACTICE PROBLEMS (Cont) • Perform each of the following operations (round to the thousandth if necessary): • a. 1472 b. 27586 c. 2712 d. 15784 • + 259 + 98764 – 1659 – 9896 • e. 158 f. 4857 g. h. • × 47 × 584

  14. PRACTICE PROBLEMS (Cont) • Evaluate each of the following: a. (5 + 1) × 3 + (2 + 4) b. 7 + 3(4 – 2) • 27 + 3(4 – 3)(12 + 6)  9 • 35 – 10 + 6

  15. Solutions • Rounding • 2,000,000 • 2,100,000 • 2,147,000 • 2,147,400 • 2,147,360 • Expanding • Twenty three thousand nine hundred fifty-six • Nine hundred sixty three thousand five hundred eighty two and forty-five hundredths

  16. Operations 1731 126350 1053 5888 7426 2836488 886.167 514.125 Operations 24 13 29 31 Solutions

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