## 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) x^{2} (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 30^{0}, 50^{0} and 100^{0}

- 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