Multiplication and Division

[Anjali303]

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!

 

[JeffM]

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

$\displaystyle multiplicative\ inverse\ of\ (1 + a)\ is\ \dfrac{1}{1 + a} = 1 - \dfrac{a}{1 + a} \ne (1 - a)\ unless\ a = 0.$

 

[HallsofIvy]

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!

"increasing by 20%" is multiplying by 1.20. Dividing by .8 is multiplying by 1/.8= 1.25. The only question is why you think they should be the same. They will differ by 5% of whatever number you are working with.

 

[lookagain]

Guess it's time to invite the Golden Ratio to step in:

3500 / ~1.618 = ~2163

3500 * ~-.618 = ~2163 ABSolutely! . . . No, it equals ~ -2163.

.

 

[lookagain]

3500 / ~1.618 = ~2163

3500 * ~-.618 = ~2163 ABSolutely!

You need another coffee too, lookagain:
you missed my "ABS (absolute value)".

I missed nothing here. Either edit it or be held accountable for
repeat remarks on it. The "ABSolutely" remark doesn't negate the
negation.

 

[lookagain]

Sorry, but the whole post was meant as a joke; only you didn't get it.

Whole post!? Hardly. It helps to show that the Golden Ratio
and its multiplicative inverse differ by 1 (or -1 depending on the
order of the subtraction).

 

[Bob Brown MSEE]

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.

Please help!

Increasing by a % is not reversed by reducing by the same %
You may enjoy the apparent contradiction as posed (Click Here)

 

[lookagain]

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Please help!

Example:

If you decrease a speed of 100 mph by 50%, it will become 50 mph.

If you increase a speed of 100 mph by 50%, it will become 150 mph.

And 100 mph is the average of each newer speed.

- - - - -

Now, suppose you decrease a speed of 100 mph by 50% and it becomes
50 mph.

But, if you increase the speed of that result of 50 mph by 50%, it becomes
75 mph. The average of those two speeds is less than 100 mph.