**Symbol representation**

We use symbols to represent quantities of specific items to formulate algebraic expressions and/or equations for computation.

Formulation of an algebraic expression and/or equation is to determine the relationship of the items and presenting their interaction behaviors in mathematics sentences.

**The Pictorial Symbol **

Sarin’s mother buys a paper bag of oranges from the supermarket. There are 5 oranges in the paper bag.

Now, if Sarin’s mother buys 2 paper bags of oranges and there are 5 oranges in each bag. There are 2 paper bags and 10 oranges in total. The picture representation of the number of oranges she buys can be as below.

**The Letter (Alphabetical Character) Symbol **

Instead of using pictorial symbols, we can use letters or Alphabetical Characters as symbols.

**Letters or Alphabetical Characters** : Characters a to z, A to Z. …

Letter symbols are ease to use as they can be read and write. It is simplicity and understandable.

If we replace the picture of the paper bag with a letter “P” and the picture of the orange with a letter “N”

** The number of oranges that Sarin’s mother buys = P × N**

Since the quantities of oranges in each bag from the supermarket always 5 numbers, “N” can be replace by 5 and the total number of oranges is depending on the number of bags of oranges that Sarin’s mother buys from the supermarket.

** The number of oranges that Sarin’s mother buys = P × 5 = 5P**

The above statement is a simple equation.

Symbol “P” is a variable number and “5P” is simple algebraic expression.

If Sarin’s mother buys 6 paper bags of oranges, then,

P = 6

The number of oranges that Sarin’s mother buys = 5P = 5 × 6 = 30

**Example of simple algebraic expressions**

1) 5P

2) N × P

3) 3N + 2

4) N + P

5) 3P + 4N – 5

**Example of simple equations (single order equation)**

1) N + P = 6

2) 3P + 4N = 43

3) 5P = N

4) 3N + 2 = 7P + 8

The pineapples and pears equation

Express using letter symbols,

The equation can be rewrite as below

The total number of pears = 3 × 14 = 42

**Computation of algebraic expression (Simplification of algebraic expression)**

a. Addition and Subtraction

Examples

1) N + N + N

= 3N

2) 2N + 3N

= (2 + 3)N

= 5N

3) N + N + 3

= 2N + 3

4) N + N + 4

= 2N + 4

= 2(N +2)

5) 4N – 3N

= (4 – 3)N

= N

6) 2N + 6N – 5N

= (2 + 6 – 5)N

= 3N

7) 3N + 4P + N

= 4N + 4P

= 4(N + P)

8) 3N + 4P – N

= 2N + 4P

= 2(N + 2P)

9) 3N + P – N + 3

= 2N + P + 3

10) N + 1/3 N

= (1 + 1/3) N

= 4/3 N

11) N – ¼ N

= ¾ N

b. Multiplication and Division

Examples

1) 3 × N = 3N

2) 3 × 2N = 6N

3) 3 ÷ N = 3/N

4) N ÷ 3 = N/3

5) 2N ÷ P + 3 = 2N/P + 3

**Computation of equation (Simplification of equation)**

Eg. 3N + 4P + 6 = 66

Math Model

Simplified model

Simplified equation (Answer)

3N + 4P = 60

Eg. 2A – 3B – 6 = 60

Math Model

Simplified model

Simplified equation (Answer)

2A = 3B + 66

Extra to note:

- If you know the value of
**A**, you can solve the equation and determine what the value of**B**is. - If you know the value of
**B**, you can solve the equation and determine what the value of**A**is. - Based on the simplified model, if you can divide A & B to equal number of units, you can compute the values of
**A**and**B**by determine the value of a unit.