Yeah that does. I’ve been doing some linear equation problems with fractional coefficients today and have been doing fine.
Purple highlighter is the problem and yellow highlighter is solution. Green arrows are steps.
Why did you want to split 11/5 up into 2 and 1/5?
I think it’s because it was the first option that occurred to me. It was so I could subtract the 1 from the 2, instead of converting the 1 to 5/5, which for some reason didn’t seem easier? I made the decision v quick.
Hm I’m kind of contradicting myself there. I think I just quickly made the decision between converting the fraction to a mixed number or not, and then proceeded.
Usually you want to reduce terms, and only split them up if there’s a specific reason to.
And usually you want to get more things to use the same denominator (unless you’re going to be able to get rid of that denominator).
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What do you think about tutoring so far?
I’m enjoying it and feeling good about continuing it. I also haven’t had trouble integrating it into my life.
I’m happy with how attentive you’ve been. It seems like I can sit down and work on something each day and rely on you to engage me.
I wouldn’t mind your thoughts on whether you are getting enough information from me about what I am doing. Keeping track of my time and what I am doing throughout the day explicitly is new to me, but it’s a skill I want to have.
Log for yesterday:
I spent about ~4hrs on math yesterday including;
32 linear equation questions over two worksheets with one error, so ~96% accuracy.
I also looked into Alcumus on AoPS Online after seeing it mentioned in Eternity’s tutoring thread and was playing around there with linear equations and some more basic stuff.
Today I am going to start looking into systems of linear equations.
Do you know the cause of the error?
I want to be clear about expectations and say I don’t guarantee replying so much/often. That’s like a bonus that people might get sometimes. But if needed we can use more longer term projects, like reading a book, so you have stuff available to work on.
Sure. I understand.
Here was my error:
I fully intended to multiply the -6 by the reciprocal of -3/4, which I half did because I got the numerator of 24 correct. My guess is I just lapsed in concentration. But I’m not sure. Substituting my answer into the original equation would’ve likely shown me my error, but I am only doing that every couple of questions, or when my answer seems particularly ‘strange’. It didn’t seem strange to me I guess because 24 also divides 4 perfectly. If I made sure to do that each time I would’ve caught the mistake.
I think you’re skipping too many steps there. Either actually write out the 4/3 on both sides to multiply by it or else multiply by 4 first and then divide by 3 as a second step.
Did 20-21 problems (one accidental double) to practise writing out more of the steps. I got two wrong due to dropping negative signs :/
good enough for now
I have been away from my computer for 3 days so was unable to do my typing test on Tuesday. I’ll do that today.
I’ve just spent ~2hrs on systems of equations today. I did a worksheet of 8 simple problems, and the problem you gave to Eternity in their tutoring topic. I got them all correct.
Before researching systems of equations I did some with just using substitution and simplifying. Then I learned the method of subtracting equations, which I practised using on the worksheet problems.
Here is some of my working for the worksheet problems:
Good job. Do some more including, when you feel ready, some harder ones with fractions. Then when you feel ready, try some word problems, similar to what Eternity has been doing, using my 3 section method.
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Are you aware that subtracting equations can be viewed as subtracting the same amount from both sides (which also works with addition, multiplication, etc.)? It’s not a special case. It can also be achieved by substitution.
Yeah I am. I just hadn’t considered it as a method.
I knew you could subtract/multiply/etc by whole expressions already. So it makes sense that you can do it with equations because they show an equality between expressions.
Spent ~1.5 hr doing some with fractions. Did 7 problems. All correct. I’ll move on to word problems tomorrow.
These problems should go a lot faster than that. Under 5 minutes, not nearly 15. It sounds like you aren’t very comfortable with them yet and need more practice.
Also can you explain the generic method to follow for how to solve a system of 5 or more equations?
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These problems should go a lot faster than that. Under 5 minutes, not nearly 15. It sounds like you aren’t very comfortable with them yet and need more practice.
Yeah sure. I’ve attached a problem I just did so you can see my working. It took ~16 mins again. I got an error of dropping a negative that I found when checking my answers. That slowed me down a few minutes.
Also can you explain the generic method to follow for how to solve a system of 5 or more equations?
I am not sure about 5 or more but I can’t see how that’d be different than two. Hmm. I’d rearrange /add/subtrac them with the goal of eliminating most variables so I can have expressions in terms of single variables. Then I can solve for those variables. I don’t think I can explain it well actually.