Possibly silly question about writing fractions

[yvonne]

This may be completely trivial, but I'm beginning to wonder if it could be problematic down the road...

I'm helping a friend's student with Saxon 7/6. He writes his fractions with a slanted line rather than a horizontal line and said that was fine with his math teacher last year. Although this student is incredibly neat, (to the point of putting my printing and writing of digits to shame!), it seems like using a slanted line might be confusing later as he gets into algebra.

 

Does it matter at all?  Would you ask him to use a horizontal line for math? 

 

Thanks!

[Tanaqui]

So long as he doesn't confuse his numerator and denominator, I'd let him do it.

When he gets to algebra, you or whoever can explain that it's a little confusing to set up fractions in the form of 10 + 2x/6-4. At that point, it will be self-evident.

[MomsintheGarden]

I would nip it in the bud now. Learning algebra may be challenging enough without having to break that habit.

[Slache]

I do that too. My division lines are longer. It's fine for me.

[kiana]

I think the diagonal line is fine when you're working with numeric fractions as long as he knows and recognizes that a horizontal line also makes a fraction.

 

When he gets to algebra, you or whoever is teaching him then can explain that it should not be used when either the numerator or denominator contains more than one term. 

[Janeway]

This may be completely trivial, but I'm beginning to wonder if it could be problematic down the road...

 

I'm helping a friend's student with Saxon 7/6. He writes his fractions with a slanted line rather than a horizontal line and said that was fine with his math teacher last year. Although this student is incredibly neat, (to the point of putting my printing and writing of digits to shame!), it seems like using a slanted line might be confusing later as he gets into algebra.

 

Does it matter at all? Would you ask him to use a horizontal line for math?

 

Thanks!

I always preferred the slanted lines.

[Ellie]

I have always written fractions with a slanted line.

[Rebel Yell]

I have always preferred a slanted line for simple fractions such as 1/4 or 1/10. But anything more complicated as would be in an algebra problem then ALL the things should have a horizontal line for consistency.

 

Although, one exception that helped one of mine wrap her head around things was to use the slanted fraction, with a longer horizontal line showing division of a fraction by a fraction. It helped her keep her numbers straight in her mind until she mastered the concept.

 

Like this, hoping I can show it right for "One fourth divided by one half":

 

1/4

____

 

1/2

 

 

 

Because

1

_

4

__

1

_

2

 

 

Would often get confused as to which line was which

Edited October 7, 2016 by Rebel Yell

[yvonne]

Thanks, everyone! 

 

Such a small thing! But, I do hate to arbitrarily ask someone change the way he does something.  MomsintheGarden makes a good point about algebra possibly being difficult enough without the risk of added confusion over which terms are in the numerator/denominator. The student is very practical. I'll show him a few examples of how a slanted line could be confusing later. I think he'll opt to change now.

 

(So, now I'm curious.... Did those of you who use slanted lines do it differently when you were doing algebra or when you were teaching your children algebra?)

Thanks, again!

[Ellie]

I have always preferred a slanted line for simple fractions such as 1/4 or 1/10. But anything more complicated as would be in an algebra problem then ALL the things should have a horizontal line for consistency.

 

Although, one exception that helped one of mine wrap her head around things was to use the slanted fraction, with a longer horizontal line showing division of a fraction by a fraction. It helped her keep her numbers straight in her mind until she mastered the concept.

 

Like this, hoping I can show it right for "One fourth divided by one half":

 

1/4

____

 

1/2

 

 

 

Because

1

_

4

__

1

_

2

 

 

Would often get confused as to which line was which

 

:iagree:

[kiana]

(So, now I'm curious.... Did those of you who use slanted lines do it differently when you were doing algebra or when you were teaching your children algebra?)

Thanks, again!

 

When I teach algebra, I will still frequently use it for a numerical fraction in isolation. For example, if I say 1/3 of the students in a class were female, I will use the slanted one because it is easier to typeset and more legible when either handwritten or typeset. When I'm emailing my students, I also use it for an algebraic fraction, but when I'm doing that I enclose the entire numerator/denominator in parentheses. For example, you will never see me write something like 1/2x, because that is ambiguous as to whether I meant (1/2) x or 1/(2x).

 

I actually think that it's important for students to also learn how to write them correctly with a slanted line, as one of the large problems I see with my students is that they do not correctly evaluate expressions such as (ln 5 + ln 3)/(ln 2 - ln 5) in their calculators, writing instead ln 5 + ln 3/ln 2 - ln 5.

[kiana]

I have always preferred a slanted line for simple fractions such as 1/4 or 1/10. But anything more complicated as would be in an algebra problem then ALL the things should have a horizontal line for consistency.

 

Although, one exception that helped one of mine wrap her head around things was to use the slanted fraction, with a longer horizontal line showing division of a fraction by a fraction. It helped her keep her numbers straight in her mind until she mastered the concept.

 

Hijacking OP's thread, but one thing I've had success with on this was using a highlighter on the big fraction. 

[Bambam]

I've always used slanted lines for my fractions. If the denominator is more complicated, then I use parenthesis around it. I'm not sure what the problem is. When you are writing it, you adjust placement, line lengths, etc so that everything is clear. 

[Rebel Yell]

I've always used slanted lines for my fractions. If the denominator is more complicated, then I use parenthesis around it. I'm not sure what the problem is. When you are writing it, you adjust placement, line lengths, etc so that everything is clear.

Not every kid has the best handwriting to keep everything neat and perfect, even when they are truly trying harder than their absolute best to be careful.

 

When I correct my kids work, if it seems to be a problem reading/seeing the line, I will highlight the line for them.

[Arcadia]

(So, now I'm curious.... Did those of you who use slanted lines do it differently when you were doing algebra or when you were teaching your children algebra?)

Hubby and I use slanted lines all the way to engineering calculus. I guess none of the exam markers had issues since we both had good grades for Cambridge exams and in college. My boys write it whichever way they want for algebra as long as there is no confusion. That means that the working for one question could have both straight and slanted lines for fractions. They just add brackets/parenthesis if it is likely to be confusing. We use blank paper for math.

I just check the AP calculus exam sample and the space for writing the answer is unlined which suits my kids just fine.

[Arcadia]

Below are exam answer samples from the same Cambridge math exam (no multiple choice) just different sections, one with straight lines for fractions and one with slanted lines. I find it faster for me to write fractions as slanted lines as it is hard to estimate for straight lines, but I need a ruler to draw straight line for fractions and matrices during exams so someone else may not have the problem.

 

Straight line sample.

http://www.cie.org.uk/images/191578-june-2014-mark-scheme-13.pdf

 

Slanted line sample

http://www.cie.org.uk/images/191586-june-2014-mark-scheme-23.pdf

 

ETA:

I used slanted lines for chemistry and physics exams too.

Edited October 8, 2016 by Arcadia

[JoJosMom]

I have always written fractions with a slanted line.

 

And you're the Queen, so you win.

 

Even if the Lesser Mortals don't understand.

 

[daijobu]

I prefer horizontal lines, especially when solving tricky math problems.  But I say if he isn't making errors, then there's no need to change.  It strikes me as such a simple change in notation that if it does become a problem in the future, he can simply switch to horizontal.  

[daijobu]

BTW, I don't think this is a silly question at all.  Notation can have a big impact on being able to see and understand what is going on.  I also prefer to have my equals signs lined up vertically, because I think that makes solutions easier to read.  

 

 

[Julie of KY]

I'd say for a simple fraction answer either is fine as long as he realized they are the same.

 

When using fractions in multiplication or other equations, I prefer the horizontal line as it makes it more clear.

[Jann in TX]

I insist on horizontal lines in ALL of my math classes-- Pre-Algebra through Algebra 2.

 

I'm fine with say, 1/3 of a cup of sugar...  but when I teach polynomial fractions (without calculators!) horizontal lines are the way to go.  I also insist on numerators in one notebook paper space and denominators in another.  This keeps the errors down (significantly!).

 

In a Physics class (I have a science degree too) I'm fine with the slant because most problems will be worked on a calculator.  I'm careful to teach putting parenthesis around numerator/denominator too...

 

 

[wapiti]

Visually, for me it's far easier to multiply and divide with fractions using a horizontal line.  Slanted lines introduce an additional element of sequential(?) tedium for me that I really don't care for.

 

I like to do things like this:

 

1           4               1    x    4

__    x   __     =      _________

7           5               7    x    5

 

 

Even without that intermediate step of a giant numerator and denominator, for me, visually, horizontal lines are much more efficient for getting to a solution than 1/7 x 4/5.