You know how to solve the tasks:
| 1. | Write down a + b for a=12 and b=15! | 12+15 = 27 | ||||
| 2. | Write down (a+b+c)/2 for a=10, b=12, c = 6! | (10+12+6)/2=14 | ||||
| 3. | Write down a·b for a=6, b= 10! | 6·10=60 |
Wherever in a given task a certain general number appears, its value is the same!
The Frenchman Vieta (1540 - 1603) has discussed the logic of these numbers and developed the theory of numbers - arithmetic (arithmos = Greek word for number).
You know that: 3 + 4 + 1= 4 + 3 + 1 = 1 + 3 + 4 and that in terms of general numbers: a + b + c = a + c + b = c + b + a. Hence you have the general rule:
The sequence of the terms in a sum is arbitrary.
You also know that 20 - 3 - 5 = 20 - 5 - 3 and a + b - c = a - c + b with the general rule:
The sequence of negative terms in an expression is arbitrary.
It only holds if a + b is greater than c: a+ b > c!
You also know that 5 · 4 = 4 · 5 and a · b = b · a or a · b · c = a · c · b = . . . with the rule
The sequence of factors in a product is arbitrary.
So far, we have seen numbers, followed by laws in general form. Entire groups of problems can now be solved by a single formula.
Task: Compute p % of k Baht!
The interest for 100 Baht is p
Baht,
for 1 Baht p/100 Baht
for k Baht p·k/100
Baht.
Denoting the answer by x, you find the percentage rule:
x = k·p/100.
Order the symbols in the numerator alphabetically, that is, write k·p instead of p·k! You can do so because the sequence of factors in a product is arbitrary. You can now solve all percentage problems by giving k and p any values.
Example: Find 4% of 135 Baht. You set k = 135, p = 4 and obtain
x = 135·4/100 = 5.40 Baht.