1. ABC/ Mathematics / Chapter 1 / TP 1 - 1 / Rev 1 © 2003 General Physics Corporation OBJECTIVES 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.

2. ABC/ Mathematics / Chapter 1 / TP 1 - 2 / Rev 1 © 2003 General Physics Corporation REPRESENTATION OF NUMBERS Fig 1-1

3. ABC/ Mathematics / Chapter 1 / TP 1 - 3 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-1 What symbol should be used to represent the number of objects below?

4. ABC/ Mathematics / Chapter 1 / TP 1 - 4 / Rev 1 © 2003 General Physics Corporation DECIMAL NUMBERS AND PLACES Fig 1-2

5. ABC/ Mathematics / Chapter 1 / TP 1 - 5 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-2 The magnitude of 54,321 is: DigitPlace Value 5  10,000=50,000 4  1,000=4,000 3  100=300 2  10=20 1  1=1 Sum=54,321

6. ABC/ Mathematics / Chapter 1 / TP 1 - 6 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-3 The magnitude of 68,095 is: DigitPlace Value 6  10,000=60,000 8  1,000=8,000 0  100=000 9  10=90 5  1=5 Sum=68,095

7. ABC/ Mathematics / Chapter 1 / TP 1 - 7 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-4 53addend +18addend 71sum Example 1-4 Example 1-5 1carry 53addend +18addend 71sum Ex 1-5

8. ABC/ Mathematics / Chapter 1 / TP 1 - 8 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-6 53 + 18 = 18 + 53 53 + 18 = 71 18 + 53 = 71 Two numbers may be added in either order and the result is the same sum.

9. ABC/ Mathematics / Chapter 1 / TP 1 - 9 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-7 Combine 3 + 5 + 7 3 + 5 = 8 ; 8 + 7 = 15 Or 3 + 7 = 10 ; 10 + 5 = 15 Or 5 + 7 = 12 ; 12 + 3 = 15 Addends may be combined in any order and the result is the same sum.

10. ABC/ Mathematics / Chapter 1 / TP 1 - 10 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-9 Ex 1-8 53minuend –18subtrahend 35difference Example 1-8 Example 1-9 Borrow 10 Units 53  4 1 3 –18–1 8 3 5

11. ABC/ Mathematics / Chapter 1 / TP 1 - 11 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-10 The commutative law does not apply to subtraction. 53 – 18  18 – 53

12. ABC/ Mathematics / Chapter 1 / TP 1 - 12 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-11 Check 53 minuend 35 difference – 18 subtrahend +18 subtrahend 35 difference 53 minuend

13. ABC/ Mathematics / Chapter 1 / TP 1 - 13 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-13 Example 1-12 3multiplicand  7multiplier 21product Example 1-13 Commutative Law 3  7 = 7  3 Associative Law 2  3  5 = (2  3)  5 = 2  (3  5) = (2  5)  3 Ex 1-12

14. ABC/ Mathematics / Chapter 1 / TP 1 - 14 / Rev 1 © 2003 General Physics Corporation Example Distributive Law 2 (3 + 5) = 2 (8) = 16 2 (3) + 2 (5) = 6 + 10 = 16 Ex 1-14

15. ABC/ Mathematics / Chapter 1 / TP 1 - 15 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-16 Example 1-15 Example 1-16 Ex 1-15 28  4 = 7 Dividend  Divisor = Quotient Quotient Divisor

16. ABC/ Mathematics / Chapter 1 / TP 1 - 16 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-17 28  4 = 7 Dividend  Divisor = Quotient Check: 4  7 = 28 Divisor  Quotient = Dividend

17. ABC/ Mathematics / Chapter 1 / TP 1 - 17 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-18 Quotient 7  r1  Remainder Divisor   Dividend

18. ABC/ Mathematics / Chapter 1 / TP 1 - 18 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-19 29  4 = 7 r1 Dividend  Divisor = Quotient + Remainder Check: 4  7 = 28 Divisor  Quotient = Check number 28 + 1 = 29 Check number + Remainder = Dividend The answer checks.

19. ABC/ Mathematics / Chapter 1 / TP 1 - 19 / Rev 1 © 2003 General Physics Corporation Example Distributive Law (8 + 12)  4 = (20)  4 = 5 (8)  4 + (12)  4 = 2 + 3 = 5 Ex 1-20

20. ABC/ Mathematics / Chapter 1 / TP 1 - 20 / Rev 1 © 2003 General Physics Corporation BINARY NUMBERS AND PLACES Fig 1-3

21. ABC/ Mathematics / Chapter 1 / TP 1 - 21 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-21 The decimal equivalent of 10110 is: DigitPlace Value 1  16=16 0  8= 0 1  4= 4 1  2= 2 0  1= 0 Sum=22

22. ABC/ Mathematics / Chapter 1 / TP 1 - 22 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-22 The decimal equivalent of 10001 is: DigitPlace Value 1  16=16 0  8= 0 0  4= 0 0  2= 0 1  1= 1 Sum=17

23. ABC/ Mathematics / Chapter 1 / TP 1 - 23 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-23 111 2 +100 2 1011 2

24. ABC/ Mathematics / Chapter 1 / TP 1 - 24 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-24 Add 111 2 + 100 2 111 2 +100 2 ??? 0 2 +1 2 = 1 2 111 2 +100 2 ??1 2 1 2 + 0 2 = 1 2 111 2 +100 2 ?11 2 1 2 + 1 2 = 10 2 111 2 +100 2 1011 2

25. ABC/ Mathematics / Chapter 1 / TP 1 - 25 / Rev 1 © 2003 General Physics Corporation EXAMPLE 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. 111 2 DigitPlace Value 1×4=4 1×2=2 1×1=1 Sum=7

26. ABC/ Mathematics / Chapter 1 / TP 1 - 26 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-24 100 2 DigitPlace Value 1 ×4=4 0 ×2=0 0 ×1=0 Sum=4 Sum = 7 + 4 = 11 1011 2 DigitPlace Value 1 ×8=8 0 ×4=0 1 ×2=2 1 ×1=1 Sum=11 The two sums agree.

27. ABC/ Mathematics / Chapter 1 / TP 1 - 27 / Rev 1 © 2003 General Physics Corporation TYPICAL BASIC SCIENTIFIC CALCULATOR Fig 1-4

28. ABC/ Mathematics / Chapter 1 / TP 1 - 28 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-25 Add 53 and 18 53 + 18 = ? Therefore, 53 + 18 = 71

29. ABC/ Mathematics / Chapter 1 / TP 1 - 29 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-26 Add 25 and 78 25 + 78 = ? Therefore, 25 + 78 = 103

30. ABC/ Mathematics / Chapter 1 / TP 1 - 30 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-27 Subtract 18 from 53. 53  18 = ? Therefore, 53  18 = 35

31. ABC/ Mathematics / Chapter 1 / TP 1 - 31 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-28 Subtract 79 from 108. 108  79 = ? Therefore, 108  79 = 29

32. ABC/ Mathematics / Chapter 1 / TP 1 - 32 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-29 Multiply 3 and 7. 3  7 = ? Therefore, 3  7 = 21

33. ABC/ Mathematics / Chapter 1 / TP 1 - 33 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-30 Multiply 53 and 26. 53  26 = ? Therefore, 53  26 = 1,378

34. ABC/ Mathematics / Chapter 1 / TP 1 - 34 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-31 Divide 28 by 7. 28  7 = ? Therefore, 28  7 = 4

35. ABC/ Mathematics / Chapter 1 / TP 1 - 35 / Rev 1 © 2003 General Physics Corporation EXAMPLE Ex 1-32 Divide 625 by 25. 625  25 = ? Therefore, 625  25 = 25