Sarin learns Symbol, Algebra and Equation in school (Math Concept)

Standard

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.

ALG-1

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.

ALG-2

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

ALG-3

Express using letter symbols,

ALG-4

The equation can be rewrite as below

ALG-5

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

ALG-6

            Simplified model

ALG-7

            Simplified equation (Answer)

            3N + 4P = 60

Eg.       2A – 3B – 6 = 60

            Math Model

ALG-8

            Simplified model

ALG-9

            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.
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