UNIT 1: WHOLE NUMBERS

1
UNIT 1 WHOLE NUMBERS

• The value of any digit depends on its place
  value

• Place value is based on multiples of 10 as
  follows

HUNDRED THOUSANDS
TEN THOUSANDS
UNITS
TENS
HUNDREDS
THOUSANDS
MILLIONS
2
EXPANDED FORM

• Place value held by each digit can be emphasized
  by writing the number in expanded form

• 9,254 can be written in expanded form as

(9 1000) (2 100) (5 10) (4 1)
3
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, drop that digit
  and all following digits replace with zeros
• If digit to right is 5 or more, add 1 to the
  digit in the place to which you are rounding.
  Drop all following digits and replace with zeros

4
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

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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
• Write 4 in units place value and carry the one

1538 2136
367
4

• Continue adding from right to left

6
SUBTRACTION

• Align number to be subtracted under the other
  number as shown line up digits that hold the
  same place value

• Start at the right and work left 7 4 3

5437 954

• Since 5 cannot be subtracted for 3, you need to
  borrow from 4 (making it 3) and add 10 to 3
  (making it 13)

3
548

• Now, 13 5 8 13 9 4 and 5 0
  5

7
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

8
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

• Bring down the 6

100

• 106 ? 25 4 write this above 6

6

• Multiply 25 4 100 write this under 106

• Subtract 106 100 6 this is the remainder

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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
208 8

• Multiply next

200

• Subtract last

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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

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PRACTICE PROBLEMS CONTINUED

• Perform each of the following operations
• a. 1472 b. 27586 c.
  2712 d. 15784
• 259 98764
  1659 9896
• e. 158 f. 4857 g.
  h.
• 47 584

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PRACTICE PROBLEMS CONTINUED

• Evaluate each of the following
• a. (5 1) 3 (2 4)
• b. 7 3(4 2)
• c. 27 3(4 3)(12 6) ? 9