Hi!
I have a query and it may sound retarded.
I am going to post an example of a sum instead of explaining.
3500/0.8 =
4375
3500*0.2 = 700 ; 3500 +700=
4200
I have calculated the final answers based on increasing it by 20%. When I multiply I use 0.2 and then add it to the main amount. And if I divide , I do it by 0.8.
Shouldn't both the answers be more closer to each other? The difference becomes massive when I use it for bigger numbers. What is the theory behind this?
Please help!
I am not absolutely sure that I understand your question so I apologize if my answer is off the mark. Furthermore, I do not know whether you know algebra or not. I shall try to answer without much algebra.
What you seem to be asking is why \(\displaystyle 3500 + (0.2 * 3500) = 3500 * 1.2 = 4200 \ne \dfrac{3500}{0.8} = 4375.\)
After all, \(\displaystyle 1 - 0.2 = 0.8\ and\ 1 + 0.2 = 1.2.\) The two numbers are equally distant from one and so have a form of symmetrical relationship.
This is an intelligent question and does not sound retarded at all.
Every real number except 0 has a unique multiplicative inverse, also known as a reciprocal. A number multiplied by its multiplicative inverse equals 1. So for example
\(\displaystyle 3 * \dfrac{1}{3} = 1\) means that 1/3 is the multiplicative inverse of 3 and 3 is the multiplicative inverse of 1/3. They form a pair of multiplicative inverses. Got the concept?
If I multiply any number by a non-zero number I get the same answer as I would by dividing the first number by the second number's multiplicative inverse.
For example, \(\displaystyle 27 * \dfrac{1}{3} = 9 = 27 \div 3.\)
How do you find the multiplicative inverse (also called the reciprocal) of a number? Very easy. If it is a fraction, invert it. If it is not a fraction, turn it into a fraction and then invert.
Example: \(\displaystyle multiplicative\ inverse\ of\ \dfrac{1}{3} = \dfrac{3}{1} = 3.\)
Example: \(\displaystyle multiplicative\ inverse\ of\ 3 = multiplicative\ inverse\ of\ \dfrac{3}{1} = \dfrac{1}{3}.\)
\(\displaystyle 0.8 = \dfrac{8}{10}\ so\ the\ multiplicative\ inverse\ of\ 0.8\ is\ \dfrac{10}{8} = 1.25 \ne 1.2.\)
You took a symmetry related to addition and subtraction and thought it turned into a symmetry of multiplication and division. Those symmetries are not connected. Here comes the algebra
\(\displaystyle multiplicative\ inverse\ of\ (1 + a)\ is\ \dfrac{1}{1 + a} = 1 - \dfrac{a}{1 + a} \ne (1 - a)\ unless\ a = 0.\)
