ALGEBRAIC PROCESSES

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

1. “=” means is equal to”

Example: 13 – 6 = 7 means thirteen minus six is equal to seven

2. “>” means is greater than”

Example: 18 > 10 means eighteen is greater than ten”

3. “<” means is less than”

Example:  -10 < 2 mean negative ten is less than two

4. “ ” means is approximately equal to”

Example:   is approximately equal to 3.142 that is  3.14

5. “ ” means not equal to”

Example:  2  3 means two is not equal to three.

Exercise

1. Write the following using symbols
2. 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

= 39^o

Exercise:  The greatest of 5 consecutive even numbers is 2a.  What is the sum of all the five numbers?

 

See also

APLLICATION OF BINARY NUMBERS

BINARY NUMBERS

SIMPLE EQUATION AND VARIATION

SQUARES OR POWERS OF NUMBERS

LOGARITHMS OF WHOLE NUMBERS