Transcript UNIT 1: WHOLE NUMBERS

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
TEN
MILLIONS THOUSANDS THOUSANDS THOUSANDS HUNDREDS TENS UNITS
2 ,
5
3
7 ,
6
1
5
2
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
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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
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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
1538
+ 2136
3674
– Add digits holding same place
value, starting on right
8 + 6 = 14
– Write 4 in units place value and carry
the one
– Continue adding from right to left
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SUBTRACTION
 Align number to be subtracted under the
other number as shown; line up digits
that hold the same place value
5837
– 654
5183
– Start at the right and work left: 7 – 4 = 3
– Since 5 cannot be subtracted from 3, you
need to borrow from 8 (making it 7) and
add 10 to 3 (making it 13)
– Now, 13 – 5 = 8; 7 – 6 = 1;
5–0=5
and
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MULTIPLICATION
 Write numbers to be multiplied as shown;
line up digits that hold the same place
value
2153
× 345
10765
8612
6459
742785
– 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
– Follow same procedure with
hundreds digit (3)
– Add to obtain final product
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DIVISION
 Write division problem with divisor
outside long division symbol and
dividend within symbol
54 r 6
25 1356
125
10 6
100
6
•
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
•
•
•
•
•
•
Multiply: 25 × 5 = 125; write this under 135
Subtract: 135 – 125 = 10
Bring down the 6
106  25 = 4; write this above 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.
2.
3.
Parentheses
Multiplication and division from left to right
Addition and Subtraction from left to right
Evaluate: (9 + 4) × 16 – 8
= 13 × 16 – 8
=
208 – 8
=
200
 Do the operation in parentheses
first
 Multiply next
 Subtract last
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ORDER OF OPERATIONS

“PEMDAS” or “Please Excuse My Dear
Aunt Sally” are other pneumonic ways to
recall.
1.
2.
3.
4.
5.
6.
Parenthsis
Exponents
Multiply
Divide
Add
Subtract
Worked left to right if all that is left in the
problem
Worked left to right if all that is left in the
problem
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PRACTICE PROBLEMS
1. Round 2,147,359 to each of the following place
values:
MILLIONS
HUNDRED
THOUSANDS
THOUSANDS
HUNDREDS
TENS
2. Write each of the following in expanded form:
a. 23,956
b. 963,582.45
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PRACTICE PROBLEMS (Cont)
3. Perform each of the following operations
(round to the thousandth if necessary):
a. 1472
+ 259
b. 27586
+ 98764
c. 2712
– 1659
d. 15784
– 9896
e. 158
× 47
f. 4857
× 584
g. 6 5317
h. 32 16452
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PRACTICE PROBLEMS (Cont)
4. Evaluate each of the following:
a. (5 + 1) × 3 + (2 + 4)
b. 7 + 3(4 – 2)
c. 27 + 3(4 – 3)(12 + 6)  9
d. 35 – 10 + 6
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Solutions
1. Rounding
1.
2.
3.
4.
5.
2,000,000
2,100,000
2,147,000
2,147,400
2,147,360
2. Expanding
1.
2.
Twenty three thousand nine hundred fifty-six
Nine hundred sixty three thousand five
hundred eighty two and forty-five hundredths
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Solutions
3.
Operations
a.
b.
c.
d.
e.
f.
g.
h.
1731
126350
1053
5888
7426
2836488
886.167
514.125
4. Operations
a. 24
b. 13
c. 29
d. 31
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