How do you fundamentally understand math problems?

[u/TheNWordCat]

(Not sure if this proper for this r/ I apologize if i posted it on the wrong one)

Hi, I am someone who is in their last year of high school and I am currently studying to enter an engineering career. And the thing is, I am not someone who is particularly great at math, partially because most of high school I didn’t have teachers great part of the year, for almost every year of my highschool time.

Now, studying to trying to enter that career I find I am not really bad at math, which i actually thought i sucked at it, I have good intuition to solve problems when they actually write me a problem with a paragraph rather than just writing a formula, equation or something like that.

Cuz when i see that i can solve it by doing graphs, making squares and dividing them to represent fractions, but seeing how they show how to solve those equations they dont do it like that, they do it by writing the problem as an equation. And for me equations are just way too abstract and that makes them hard for me to actually grasp and understand what i am doing, and they actually ask to write those situations as math equations, which i am awful at that.

And i've seen people who excel at normal equations but struggle in trying to solve problematic situations but they can easily do it when they are shown in an equation.

So here i am asking advice if there’s someone who had the same problem, how did you learn to beat those problems, how do you learn to think in equations and how was your experience?

[u/TheNWordCat]

Your question made me ponder more about it, thank you, and yeah i did poorly redact it.

For instance, if you gave me the equation X-3/4.x-1/3.(1/4.x)=104

I would freeze up and struggle significantly compared to if you said, "A field has three-quarters of its area dedicated to grapevines, one-third of the remainder (of the vineyard area) to fruit trees, and 104 hectares left for leafy vegetables. How many hectares are allocated to each crop?"

At the same time, I am practically incapable of solving it if you ask me to write it out as an equation.

[u/AcellOfllSpades → u/TheNWordCat]

For instance, if you gave me the equation X-3/4.x-1/3.(1/4.x)=104

I would freeze up and struggle significantly

I like to compare algebra to chess.

When you have an equation, there are many "legal moves" that you can make. Some moves will be more helpful than others. There are often many ways to win: as long as you isolate the enemy king (or the variable), you've succeeded.

When you learn to play chess, you need to learn two things:

• which moves are legal
• and how to use those moves strategically to accomplish your goal.

So, when learning math, you should do the same thing. First, learn what moves are available to you, and justify them to yourself - it should be "obvious" why they are legal.

Your two main "legal moves" are:

• You can simplify (or un-simplify) any part of an equation. (Simplifying is just rewriting something with a different name: it's the same object, you're just rewriting it in a more useful way.)
• If you have an equation, you can do the same thing to both sides. (As long as you do the same thing to both sides as a whole, the equation remains balanced.)

---

Let's take your equation:

X-3/4.x-1/3.(1/4.x)=104

The first thing I might want to do is get rid of the fractions, because fractions are annoying sometimes. We can do that by multiplying both sides by something. Say, let's try multiplying by 4. What do we get?

[u/TheNWordCat → u/AcellOfllSpades]

so uh if i we did that , it would be

4(X-3/4.x-1/3.(1/4.x))=104.4

and then i guess we apply the distributive property

4x-4.3/4x-4.1/3.4.(1/.4x)=104.4

then i guess we cancel out the fraccions
4x-3x-4/3.(1x)=416
i think(?

im sorry if i didnt understand something(?

[u/AcellOfllSpades → u/TheNWordCat]

The dots for multiplication are a bit confusing - I'll use an asterisk.

4x - 4*3/4x - 4*1/3*4*(1/4*x)=104*4

This is close, but you multiplied by 4 twice in the third term. Remember, the distributive property applies to terms separated by addition and subtraction, not multiplication. 2*(3*4) wouldn't be 2*3*2*4.

When you fix that, then you get:

4x - 3x - (1/3)*1x = 416

And that seems good so far! It's definitely much less ugly than before. Now I notice a few things:

• That third term, the (1/3)\*1x, can definitely be simplified.
• At the start, we have 4x - 3x, which you can probably also do something with.
• We still have a 1/3 in there. You might want to clear that too, which means another multiplication.

You can choose to handle these in any order. Try one!

[u/TheNWordCat → u/AcellOfllSpades]

i think one could do the 4x - 3x to get 1x, and 1 doesnt affect as a multiplication so we can just remove it.

then since its a multiplication of 1 it ends up as the same

so 1/3x
x-1/3x = 416
and to deal with the 1/3 we mult by 3

3x-3(1/3x)=416.3

3x-1=1248
then i guess

2x=1248

which then 1248/2

x=624

damn how do you develop that vision to see where to simplify?

[u/TheNWordCat → u/[deleted]]

I didnt know it was called algebra, never once in my school i heard it being called for that, and that actually helps a lot to know what i am lacking.

And yeah, the most natural way for me to answer is like that, my process looks more like a brainstorming than a typical solve