Question

4 + m/8 = 3/4 = ?
(Show Work)

Answer 1

\[4+\frac{m}{8} = \frac{3}{4}\]
correct?

Answer 2

yes

Answer 3

Clear fractions... multiply everything by the LCD... which would be 8.

Answer 4

Let's see what you get after clearing fractions... or perhaps ask a question.

Answer 5

like how?

Answer 6

Why not just multiply 3/4 by 2/2

Answer 7

\[(8)(4+\frac{m}{8})=\frac{3}{4}(8)\]Distribute on the left, mulitpy by reducing on the right.

Answer 8

If you multiply 3/4 by 2/2, you'd have

\[4 + \frac{m}{8} = \frac{6}{8}\]

Answer 9

Then you could subtract m/8 from both sides afterwards.

Answer 10

Clearing fractions is a standard technique in intermediate algebra so that the student can avoid the fears that come from dealing with fractions. You can, of course, manipulate fractions, but the student usually prefers to avoid it unless absolutely necessary.

Answer 11

I was never a fan of standard techniques.

Answer 12

ok

Answer 13

So which would you like, clearing fractions, or work with them... either is totally valid.

Answer 14

That's like a 'trick question'.

Answer 15

No, really... I like fractions... either is ok.

Answer 16

You should probably ask, would you like to work with LCDs or regular algebra.

Answer 17

LCD's are regular algebra. It is strategically multiplying both sides by the same number to get a manageable result. Balancing equations are at the heart of algebra.

Answer 18

Standard techniques provide students who are below college algebra level with a sense of security. At the college algebra level, numerous methods should be presented so that the student becomes adaptable to various situations. Before that, it generally freaks them out.

Answer 19

I honestly would rather avoid calling it LCDs because it tends to confuse students.

Answer 20

You're trying to suggest that no student have problems with LCDs.

Answer 21

I can type out lowest common denominator if necessary.

Answer 22

No, I am just using the advice given to me by my employer for dealing with students at various levels. I see what students encounter in their courses every day, so I try to emply those techniques.

Answer 23

I sense that you solve problems with a highly intuitive approach supported by solid technique. I love students like you. You advance math. But I've seen scared students too. I try to help them through.

Answer 24

And in this case, I try to show students that you can apply simple algebra to solve problems. Yeah, I have all kinds of alternative methods I use.

Answer 25

We lost our student. :( I hope that she got it.

Answer 26

What a pity. I hope so.

Answer 27

Don't put me in a classroom

Answer 28

I hope that I haven't aggravated you Hero. I appreciate that contributions that I've seen you provide. I simply have an approach that I have been trained to provide. I am sometimes winging it, but at this level I have tutored many students and feel confident. Please don't believe that I hold any ill will.

Answer 29

"trained to provide". So does that mean you are not allowed to show alternative methods?

Answer 30

If I were in a classroom, I would show students the standard and alternative methods

Answer 31

And let them choose which one they prefer

Answer 32

Oh, I absolutely am, but students below college algebra level generally want to know... what is step 1... then step 2... then step 3... just like my teacher showed me or "la la la I can't hear you". It is very common at the community college level. They tune you out or lose faith if it doesn't look "just like my teacher said". At college algebra, I try to open them up. Look at it from numerous perspectives and develop a style.

Answer 33

Then I don't care what their teacher says. Their are many perspectives, choose the one that works for you. Fit the teacher enough to pass the class and move beyond.

Answer 34

Of course, I would show both methods and wouldn't forget to put "step 1" "step 2" in my presentations.

Answer 35

Some "below college level" students like the alternative methods.

Answer 36

I suspect that you appreciate the multiple perspective approach highly, but you are not in the majority. Most get scared by that.

Answer 37

And I don't mean college level exactly. I mean College Algebra level. In high school it is commonly referred to as Algebra 2.

Answer 38

I suppose Algebra II is what you teach.

Answer 39

It's just a title. You need "College Algebra" to get the associate's degree and often it is all you need for a liberal arts degree.

Answer 40

Oh, I see. To be honest, I did learn the alternative methods later on, but now I'm mad at the teachers I had for not knowing them or showing them to me. I think that students who have already mastered a certain concept could definitely benefit from alternative methods.

Answer 41

I agree. I just don't want to scare them away. I want them to learn to love it, then open the door to see more.

Answer 42

I think that there are completely alternative ways to learn this stuff that would work well. I'm just trying to work with the system that is in place.

Answer 43

This site is awesome for finding other ways.

Answer 44

I agree. I am pretty much an alternative methods geek. I'm always looking for alternative methods. One day, I might right a book with nothing but alternative methods in them.

Answer 45

That would be a great contribution. Like I said, it is people like you who advance math rather than just learn what is already there and regurgitate. I will admit that I am generally a regurgitator that admires new things to regurgitate.

Answer 46

If I ever get a totally fresh idea on my own, that satisfaction would probably put a smile on my face for years.

Answer 47

Yeah, I'm like that too. That's why I'm more than excited to show the alternative methods.

Answer 48

I always seem to develop new methods that spring from annoyance with the "by the book" methods. I'm always convinced that there is some other method that works that could be more straightforward or easier. The way I solve the fractions is one method. Then there's the method for finding the slope of a line. But I have plenty other alternative methods too.