WEEK THREE
APLLICATION OF BINARY NUMBERS
Bunch Cards: it is used in business farms, examining from boards and other organization as a solution for sorting information.
Example: suppose that a failure in a subject is represented by the digit zero. Then for any 5 subjects English, Mathematics, French, Agric and C.R.K. The number 10110 represent a pass in English, a failure in mathematics, a pass in French, a pass in agric and a failure in C.R.K.
Bunch Tape
| Letters | Decimal No | Binary Code |
| A | 1 | 1 |
| B | 2 | 10 |
| C | 3 | 11 |
| D | 4 | 100 |
| E | 5 | 101 |
| F | 6 | 110 |
| G | 7 | 111 |
| H | 8 | 1000 |
| I | 9 | 1001 |
| J | 10 | 1010 |
| K | 11 | 1011 |
| L | 12 | 1100 |
| M | 13 | 1101 |
| N | 14 | 1110 |
| O | 15 | 1111 |
| P | 16 | 1000 |
| Q | 17 | 10001 |
| R | 18 | 10010 |
| S | 19 | 10011 |
| T | 20 | 10100 |
| U | 21 | 10101 |
| V | 22 | 10110 |
| W | 23 | 10111 |
| X | 24 | 11000 |
| Y | 25 | 11001 |
| Z | 26 | 11010 |
French tapes are used to enter information and instruction into some computers.
Exercise:
- Using a letter per line code and with the words represented by the following
(a) 1 (b) 10000 (c) 100
100 101 101
100 10100 1100
10010 101 1001
101 10010 10110
10011 101
10011 10010 - Write the following in a letter per line code.
(a) S (b) D (c) A (d) S (e) E
U I N C L
N V G H I
D I E O A
A N L O S
Y E L - Code your surname in binary
WEEK 4
ALGEBRAIC PROCESSES
Objective: Use letter to generalize statements
- Interpret mathematical symbols
- Solve simple and problems
Generating statement
The following symbols are generally used in mathematics
- “=” means is equal to”
Example: 13 – 6 = 7 means thirteen minus six is equal to seven
- “>” means is greater than”
Example: 18 > 10 means eighteen is greater than ten”
- “<” means is less than”
Example: -10 < 2 mean negative ten is less than two
- ” ” means is approximately equal to”
Example: is approximately equal to 3.142 that is 3.14
- “” means not equal to”
Example: 2 3 means two is not equal to three.
Exercise
- Write the following using symbols
- M is equal to 8 (ii) y lies between 8 and 12
(iii) Twice y equals fourteen, therefore y equals seven.
OPERATION IN ALGEBRA
EXAMPLE
Write down the meaning of the following and find the values if x = 8, y = 3, z = 9
(a) 2x (b) 2 + x (c) (d) x – 5 (e) x2 (f) x + yz
Solution
(a) Multiply x by 2 (b) Add two to (c) Divide x by 2
I.e. 2 x 8 = 16 i.e. 8 + 2 = 10 = = 4
(d) Subtract five from (e) Square (f) multiply y by z
– 5 = 8 – 5 = 3 2 = 8 x 8 = 64 + yz = 8 + 3(9) = 8 + 27 = 35
Exercise: If a = 5, b = -3 and c = 2. Find the value of (a) 2a + b – c (b) 5a – 8 (c) 8ac – 2b (d)
LIKE AND UNLIKE TERMS (WORD PROBLEMS)
Examples 1: A fence is made up of 3 different bundles of length 3m each, 5 different hurdles of lengths 5m each and 2 different hurdles of length 2m each. What is the total length?
SOLUTION
Let the 3 hurdles be, y and z
Then total length force = 3x + 5y – 2z
2) A tourist walked km an hour for 3 hours on the first day and km an hour for y hours on the second day. How far did he walk in the two days?
Ans. (3x + y) km
Exercise
A family eats a loaves of bread a day. How many loaves are need for (a) M-days (b) Kweeks (c) How long will p loaves last? (a) 4m loaves (b) 28k Loaves (c) days
Use of brackets
Examples 1: The angles of a triangle measured in decrees’ are 2, 3+ 5, 4 (+ 10). What are the values of the angles?
SOLUTION
2 + (3 + 5) + 4 ( + 10) = 180
2 + 3 + 5 + 4+ 40 = 180
9x + 45 + 180 – 45
=
= 150
The angles are 300, 500 and 1000
2. The results of adding three consecutive numbers is one hundred and twenty. Find the number.
SOLUTION
Let the numbers be, + 1,+ 2
++ 1 + + 2 = 120
3 + 3 = 120
3 (+1) = 120
+ 1 + 40
+ 40 -1
= 39o
Exercise: The greatest of 5 consecutive even numbers is 2a. What is the sum of all the five numbers?