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
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
1) N + N + N
2) 2N + 3N
= (2 + 3)N
3) N + N + 3
= 2N + 3
4) N + N + 4
= 2N + 4
= 2(N +2)
5) 4N – 3N
= (4 – 3)N
6) 2N + 6N – 5N
= (2 + 6 – 5)N
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
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
Simplified equation (Answer)
3N + 4P = 60
Eg. 2A – 3B – 6 = 60
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.