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