View
213
Download
1
Category
Preview:
Citation preview
ABC/ Mathematics / Chapter 1 / TP 1 - 1 / Rev 1© 2003 General Physics Corporation
OBJECTIVESOBJECTIVES
1. Without a calculator; ADD, SUBTRACT, MULTIPLY, and DIVIDE whole numbers.
2. With an approved calculator; ADD, SUBTRACT, MULTIPLY, and DIVIDE whole numbers.
3. Without a calculator; CONVERT between decimal and binary numbers.
ABC/ Mathematics / Chapter 1 / TP 1 - 2 / Rev 1© 2003 General Physics Corporation
REPRESENTATION OF NUMBERS REPRESENTATION OF NUMBERS
Fig 1-1
123
987654
ABC/ Mathematics / Chapter 1 / TP 1 - 3 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-1
What symbol should be used to represent the number of objects below?
ABC/ Mathematics / Chapter 1 / TP 1 - 4 / Rev 1© 2003 General Physics Corporation
DECIMAL NUMBERS AND PLACES DECIMAL NUMBERS AND PLACES
Fig 1-2
5 4 3 2 1 Place Title
Place Value
Units 1
Tens 10
Hundreds 100
Thousands 1,000
Ten thousands 10, 000
ABC/ Mathematics / Chapter 1 / TP 1 - 5 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-2
The magnitude of 54,321 is:
Digit Place Value5 10,000 = 50,0004 1,000 = 4,0003 100 = 3002 10 = 201 1 = 1
Sum = 54,321
ABC/ Mathematics / Chapter 1 / TP 1 - 6 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-3
The magnitude of 68,095 is:
Digit Place Value6 10,000 = 60,0008 1,000 = 8,0000 100 = 0009 10 = 905 1 = 5
Sum = 68,095
ABC/ Mathematics / Chapter 1 / TP 1 - 7 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-4
53 addend+ 18 addend
71 sum
Example 1-4
Example 1-5
1 carry53 addend
+ 18 addend71 sum
Ex 1-5
ABC/ Mathematics / Chapter 1 / TP 1 - 8 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-6
53 + 18 = 18 + 5353 + 18 = 7118 + 53 = 71
Two numbers may be added in either order and the result is the same sum.
ABC/ Mathematics / Chapter 1 / TP 1 - 9 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-7
Combine 3 + 5 + 7
3 + 5 = 8 ; 8 + 7 = 15Or3 + 7 = 10 ; 10 + 5 = 15Or5 + 7 = 12 ; 12 + 3 = 15
Addends may be combined in any order and the result is the same sum.
ABC/ Mathematics / Chapter 1 / TP 1 - 10 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-9Ex 1-8
53 minuend– 18 subtrahend
35 difference
Example 1-8
Example 1-9
Borrow 10 Units 53 413– 18 – 1 8
3 5
ABC/ Mathematics / Chapter 1 / TP 1 - 11 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-10
The commutative law does not apply to subtraction.
53 – 18 18 – 53
ABC/ Mathematics / Chapter 1 / TP 1 - 12 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-11
Check
53 minuend 35 difference– 18 subtrahend +18 subtrahend 35 difference 53 minuend
ABC/ Mathematics / Chapter 1 / TP 1 - 13 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-13
Example 1-12
3 multiplicand 7 multiplier
21 product
Example 1-13
Commutative Law3 7 = 7 3
Associative Law2 3 5 = (2 3) 5 = 2 (3 5) = (2 5) 3
Ex 1-12
ABC/ Mathematics / Chapter 1 / TP 1 - 14 / Rev 1© 2003 General Physics Corporation
ExampleExample
Distributive Law
2 (3 + 5) = 2 (8) = 16
2 (3) + 2 (5) = 6 + 10 = 16
Ex 1-14
ABC/ Mathematics / Chapter 1 / TP 1 - 15 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-16
Example 1-15
Example 1-16
Ex 1-15
4224
2
424
28 4 = 7Dividend Divisor = Quotient
QuotientDivisor
Dividend 7 284
ABC/ Mathematics / Chapter 1 / TP 1 - 16 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-17
28 4 = 7Dividend Divisor = Quotient
Check:4 7 = 28Divisor Quotient = Dividend
ABC/ Mathematics / Chapter 1 / TP 1 - 17 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-18
Quotient 7 r1 Remainder
Divisor Dividend294
ABC/ Mathematics / Chapter 1 / TP 1 - 18 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-19
29 4 = 7 r1Dividend Divisor = Quotient + Remainder
Check:4 7 = 28Divisor Quotient = Check number
28 + 1 = 29Check number + Remainder = Dividend
The answer checks.
ABC/ Mathematics / Chapter 1 / TP 1 - 19 / Rev 1© 2003 General Physics Corporation
ExampleExample
Distributive Law
(8 + 12) 4 = (20) 4 = 5
(8) 4 + (12) 4 = 2 + 3 = 5
Ex 1-20
ABC/ Mathematics / Chapter 1 / TP 1 - 20 / Rev 1© 2003 General Physics Corporation
BINARY NUMBERS AND PLACES BINARY NUMBERS AND PLACES
Fig 1-3
1 0 1 1 0 Place Value
1
2
4
8
16
ABC/ Mathematics / Chapter 1 / TP 1 - 21 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-21
The decimal equivalent of 10110 is:
Digit Place Value1 16 = 160 8 = 01 4 = 41 2 = 20 1 = 0
Sum = 22
ABC/ Mathematics / Chapter 1 / TP 1 - 22 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-22
The decimal equivalent of 10001 is:
Digit Place Value1 16 = 160 8 = 00 4 = 00 2 = 01 1 = 1
Sum = 17
ABC/ Mathematics / Chapter 1 / TP 1 - 23 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-23
1112
+ 1002
10112
ABC/ Mathematics / Chapter 1 / TP 1 - 24 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-24
Add 1112 + 1002
1112
+ 1002
???02 +12 = 12
1112
+ 1002
??12
12 + 02 = 12
1112
+ 1002
?112
12 + 12 = 102
1112
+ 1002
10112
ABC/ Mathematics / Chapter 1 / TP 1 - 25 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-24
To check the answer convert the two addends to decimal numbers and add them in decimal numbers. Then convert the binary sum to a decimal number and compare it to the decimal sum.
1112
Digit Place Value
1 × 4 = 4
1 × 2 = 2
1 × 1 = 1
Sum = 7
ABC/ Mathematics / Chapter 1 / TP 1 - 26 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-24
1002
Digit Place Value
1 × 4 = 4
0 × 2 = 0
0 × 1 = 0
Sum = 4
Sum = 7 + 4 = 11
10112
Digit Place Value
1 × 8 = 8
0 × 4 = 0
1 × 2 = 2
1 × 1 = 1
Sum = 11
The two sums agree.
ABC/ Mathematics / Chapter 1 / TP 1 - 27 / Rev 1© 2003 General Physics Corporation
TYPICAL BASIC SCIENTIFIC CALCULATOR TYPICAL BASIC SCIENTIFIC CALCULATOR
Fig 1-4
x
x x2 x y
x y
x
CSR
n-1
n
SIN-1
EE
COS-1
10X
DRG>
TAN-1
ex
ON
P>R
R>P
DMS>DD
DD>DMS
1/x % DRG AC2nd
6.02 23
x2 SIN COS TAN CE/C
x! EE LOG LN yx
+ K ( )
STO 7 8 9 X
RCL 4 5 6 -
SUM 1 2 3 +
EXC 0 +/- =
ABC/ Mathematics / Chapter 1 / TP 1 - 28 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-25
Add 53 and 18
53 + 18 = ?
Enter Operation Display
53 + 53
18 = 71
Therefore,53 + 18 = 71
ABC/ Mathematics / Chapter 1 / TP 1 - 29 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-26
Add 25 and 78
25 + 78 = ?
Enter Operation Display
25 + 25
78 = 103
Therefore,25 + 78 = 103
ABC/ Mathematics / Chapter 1 / TP 1 - 30 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-27
Subtract 18 from 53.
53 18 = ?
Enter Operation Display
53 53
18 = 35
Therefore,53 18 = 35
ABC/ Mathematics / Chapter 1 / TP 1 - 31 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-28
Subtract 79 from 108.
108 79 = ?
Enter Operation Display
108 108
79 = 29
Therefore,108 79 = 29
ABC/ Mathematics / Chapter 1 / TP 1 - 32 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-29
Multiply 3 and 7.
3 7 = ?
Enter Operation Display
3 3
7 = 21
Therefore,3 7 = 21
ABC/ Mathematics / Chapter 1 / TP 1 - 33 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-30
Multiply 53 and 26.
53 26 = ?
Enter Operation Display
53 53
26 = 1,378
Therefore,53 26 = 1,378
ABC/ Mathematics / Chapter 1 / TP 1 - 34 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-31
Divide 28 by 7.
28 7 = ?
Therefore,28 7 = 4
Enter Operation Display
28 28
7 = 4
ABC/ Mathematics / Chapter 1 / TP 1 - 35 / Rev 1© 2003 General Physics Corporation
EXAMPLEEXAMPLE
Ex 1-32
Divide 625 by 25.
625 25 = ?
Enter Operation Display
625 625
25 = 25
Therefore,625 25 = 25
Recommended