Transcript PowerPoint Presentation 1: Whole Numbers

PRESENTATION 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:
TEN
HUNDRED
MILLIONS THOUSANDS THOUSANDS THOUSANDS HUNDREDS TENS
2 ,
6
7
8 ,
9
3
UNITS
2
ESTIMATING
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Used when an exact mathematical answer is
not required
A rough calculation is called estimating or
approximating
Mistakes can often be avoided when estimating
is done before the actual calculation
When estimating, exact values are rounded
ROUNDING
• Used to make estimates
• Rounding Rules:
o Determine place value to which the number is to
be rounded
o Look at the digit immediately to its right
 If the digit to the right is less than 5, replace that
digit and all following digits with zeros
 If the digit to the right is 5 or more, add 1 to the
digit in the place to which you are rounding.
Replace all following digits with zeros
ROUNDING EXAMPLES
•
Round 612 to the nearest hundred
Since 1 is less than 5, 6 remains unchanged
Answer: 600
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Round 175,890 to the nearest ten thousand
7 is in the ten thousands place value, so look at 5.
Since 5 is greater than or equal to 5, change 7 to
8 and replace 5, 8, and 9 with zeros
Answer: 180,000
ADDITION OF WHOLE
NUMBERS
• The result of adding numbers is
called the sum
• The plus sign (+) indicates addition
• Numbers can be added in any
order
PROCEDURE FOR ADDING
WHOLE NUMBERS
•
Example: Add 763 + 619
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Align numbers to be added as shown;
line up digits that hold the same place
value
Add digits holding the same place
value, starting on the right: 9 + 3 = 12
Write 2 in the units place value and
carry the one
PROCEDURE FOR ADDING
WHOLE NUMBERS
• Continue adding from right to
left
• Therefore,
763 + 619 = 1,382
SUBTRACTION OF WHOLE
NUMBERS
• Subtraction is the operation which
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determines the difference between
two quantities
It is the inverse or opposite of
addition
The minus sign (–) indicates
subtraction
PROCEDURE FOR SUBTRACTING
WHOLE NUMBERS
• Example:
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Subtract 917 – 523
Align digits that hold the same
place value
Start at the right and work left:
7–3=4
PROCEDURE FOR SUBTRACTING
WHOLE NUMBERS
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Since 2 cannot be subtracted from
1, you need to borrow from 9
(making it 8) and add 10 to 1
(making it 11)
Now, 11 – 2 = 9; 8 – 5 = 3
Therefore,
917 – 523 = 394
MULTIPLICATION OF WHOLE
NUMBERS
• Multiplication is a short method of
adding equal amounts
• There are many occupational uses
of multiplication
• The times sign (×) is used to
indicate multiplication
PROCEDURE FOR
MULTIPLICATION
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Example: Multiply 386 × 7
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Align the digits on the right
First, multiply 7 by the units of the
multiplicand: 7 ×6 = 42
Write 2 in the units position of the
answer
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PROCEDURE FOR
MULTIPLICATION
Multiply the 7 by the tens of the
multiplicand:
7 × 8 = 56
Add the 4 tens from the product of the
units:
56 + 4 = 60
Write the 0 in the tens position of the
answer
PROCEDURE FOR
MULTIPLICATION
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Multiply the 7 by the hundreds of
the multiplicand: 7 × 3 = 21
Add the 6 hundreds from the
product of the tens: 21 + 6 = 27
Write the 7 in the hundreds position
and the 2 in the thousands position
Therefore,
386 × 7 = 2,702
DIVISION OF WHOLE
NUMBERS
• In division, the number to be
divided is called the dividend
• The number by which the dividend
is divided is called the divisor
• The result is the quotient
• A difference left over is called the
remainder
DIVISION OF WHOLE
NUMBERS
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Division is the inverse, or opposite, of
multiplication
Division is the short method of subtraction
The symbol for division is ÷
The long division symbol is
Division can also be expressed in fraction
form such as 20
99
DIVISION WITH ZERO
• Zero divided by a number equals
zero
o For example: 0 ÷ 5 = 0
• Dividing by zero is impossible; it is
undefined
o For example: 5 ÷ 0 is not possible
PROCEDURE FOR DIVISION
• Example: Divide 4,505 ÷ 6
o Write division problem with divisor
outside long division symbol and
dividend within symbol
o Since 6 does not go into 4, divide 6 into
45.
45  6 = 7; write 7 above the first 5 in
number 4505 as shown
o Multiply: 7 × 6 = 42; write this under 45
o Subtract: 45 – 42 = 3
PROCEDURE FOR DIVISION
o Bring down the 0
o Divide: 30  6 = 5; write the 5
above the 0
o Multiply: 5 × 6 = 30; write this under
30
o Subtract: 30 – 30 = 0
o Since 6 cannot divide into 5, write 0
in the answer above the 5. Subtract
0 from 5 and 5 is the remainder
o Therefore 4505  6 = 750 r5
ORDER OF OPERATIONS
• All arithmetic expressions must be
simplified using the following order of
operations:
1.Parentheses
2.Raise to a power or find a root
3.Multiplication and division from left to right
4.Addition and subtraction from left to right
ORDER OF OPERATIONS
• Example: Evaluate (15 + 6) × 3 – 28
÷7
21 × 3 – 28 ÷ 7
Do the operation in parentheses
first (15 + 6 = 21)
63 – 4
Multiply and divide next
(21 ×3 = 63) and (28 ÷ 7 = 4)
63 – 4 = 59
Subtract last
• Therefore: (15 + 6) × 3 – 28 ÷ 7 =
59
PRACTICAL PROBLEMS
• A 5-floor apartment building has 8
electrical circuits per apartment.
There are 6 apartments per floor.
How many electrical circuits are
there in the building?
PRACTICAL PROBLEMS
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Multiply the number of apartments per
floor times the number of electrical
outlets
Multiply the number of floors times the
number of outlets per floor obtained in
the previous step
There are 240 outlets in the building