When do you not simplify in math?

[Tyrion101]

I have been studying algebra, and a good portion seems to be, getting really long equations to simple ones. My question is is there ever a time in any math where you wouldn't want to simplify? Assuming it isn't just the teacher not caring if you do.

 

[I like Serena]

I have been studying algebra, and a good portion seems to be, getting really long equations to simple ones. My question is is there ever a time in any math where you wouldn't want to simplify? Assuming it isn't just the teacher not caring if you do.

Hi Tyrion101!

Ultimately you will need to consider whether it is worth to simplify something or not.

When solving a mathematical problem, it's often wise not to simplify the answer.
Simplifying may rob you of a correct answer due to a careless mistake.
On the other hand, if your problem is not solved yet, it may be wise to simplify, so you don't drag a long complicated expression along, increasing the chance on mistakes.

A teacher may want you to simplify, just so you learn how to do it.
But ultimately it's not simplifying that's important, but solving a problem and getting the correct answer, so that for instance a bridge does not fall apart.
In other words, simplifying is a means, but not an end.

 

[symbolipoint]

I have been studying algebra, and a good portion seems to be, getting really long equations to simple ones. My question is is there ever a time in any math where you wouldn't want to simplify? Assuming it isn't just the teacher not caring if you do.

A simplified formula or expression is often easier to understand, and may be more compact making its use more efficient.

As a basic example, a problem situation you might study could lead to a fairly simple quadratic equation. The equation itself may well be very simple, taking the typical general form. Depending on what you want from this equation, you might wish to put it into standard form, maybe in order to more easily 'sketch' a graph. Converting into the standard form would require a few algebraic steps which themselves are making the equation LESS SIMPLIFIED. The standard form, although seeming to be less simplified, is still useful because of how you can use its features to make a graph manually.

 

[phlip180]

To answer briefly (and a little simplified) you would want to simplify a formula if you expect you or someone else may want to use that formula again later. Obviously if you are going to be using a formula for 100 different values, it could save a lot of time by simplifying and removing any redundancies. If you do not expect you will have to use the given formula again or you think the process of simplifying the formula would be more work than it would save, then you might choose to stick with the more complicated formula. Ultimately, it comes down to personal preference most of the time.

 

[CellCoree]

I understand the importance of simplification in math, especially in algebra. Simplifying equations allows us to more easily understand and solve complex problems. However, there are certain situations where it may not be necessary or beneficial to simplify.

One example is in advanced calculus or physics, where equations may be intentionally left in their complex form to accurately represent a physical phenomenon. In these cases, simplification may result in loss of important information or inaccuracies in the solution.

Additionally, in some mathematical proofs or theoretical concepts, it may be necessary to keep equations in their original form in order to demonstrate a specific concept or relationship.

Ultimately, the decision to simplify in math depends on the specific problem at hand and the purpose of the solution. In most cases, simplification can be helpful and is encouraged, but there are certainly times where it may not be necessary or even counterproductive.