### Fraction Myth Debunked

**by**Aleksandr Rusinov

**on**June 29, 2012

**in**Reflections

**with**No Comments »

##### Introduction

The hottest discussion topic among mathematic educators within Metropolitan College of New York revolves around the idea of what mathematic skills our students should have. The biggest concern arises when students face failure with fraction concepts. The advancement from secondary to post-secondary education demands that students should have already mastered these skills in elementary school and demonstrated computational proficiency during the Accuplacer entry examination. However, newly admitted and even some continuing students continue to struggle with concepts of fraction addition and fraction subtraction. So, many students believe that mastery of fraction skills will never be achieved. This belief is a myth.

##### How the story goes

Recognizing that these days the average MCNY student is usually a parent who works a full-time job and has very little time to spend on academic preparation for college courses, MCNY began to offer mentoring and LEC academic support services to help students recover and develop the skills necessary to succeed in college life. Further, many of these students return to post-secondary education after decades of being away from any type of formal learning environments, and, as a result, they require more time spent on mathematic remediation.

##### Where it leads

In my math classes and at the LEC, I often encounter students who need help with basic fraction addition and subtraction. For many students, fractions seem like ancient history and halfway-forgotten meaningless procedures. When students are asked to face this old foe, their historical anxieties are provoked, thus fueling the myth that mastery of skills involving fraction addition and fraction subtraction can never be achieved.

##### My Advice

To become more proficient in any mathematic problem solving concepts it is important to realize that success in mastery of problem solution skills always relies on closely observing the challenging problem. For example, if we have to solve 1 + ½, there is no need to represent 1 as ^{2}/_{2 }and do^{2}/_{2 + }½ = ^{2+1}/ _{2} = ^{3 }/ _{2} = 1 ^{1}/_{2.}

In fact 1 + ½ could be represented as 1 + 0.5 = 1.5

So, 1 + ½ = 1 ^{1}/_{2}

How did we solve this problem in decimal notation? We just added the fractional part to the whole part. We can also separate whole part and fractional part like this:

1.5 = 1 ^{1}/_{2 }= 1 + 0.5 = 1 + ½

Advancing to a more challenging problem, we can perform arithmetic separately with whole parts and fractional parts, and then combine them together.

Let’s look at this example: 3 ^{1}/_{3} – 1 ^{1}/_{2}

Working separately with whole parts and fractional parts we will see the following:

3 – 1 = 2

^{1}/_{3} – ^{1}/_{2} = ^{×2/ 1}/_{3} – ^{×3/ 1}/_{2} = ^{2}/_{6} – ^{3}/_{6} = ^{2 – 3}/_{6} = – ^{1}/_{6}

2 + (- ^{1}/_{6}) = 1 + 1 – ^{1}/_{6 }= 1 + ^{6}/_{6} – ^{1}/_{6 }= 1+ ^{6 – 1}/_{6} = 1+ ^{5}/_{6} = 1^{5}/_{6 }

Thus, 3 ^{1}/_{3} – 1 ^{1}/_{2} = 1^{5}/_{6}

If you are not yet convinced, try to solve any following problem involving fraction addition or subtraction.

##### Try It Out

For your convenience I would like to offer few exercise samples.

5 ^{1}/_{2} + 1 ^{1}/_{4} =

7 ^{1}/_{2} – 1 ^{1}/_{3} =

9 – 1 ^{1}/_{2} =

4 ^{1}/_{3} + 2 =

Solutions will be included in my next post. Keep up your good work!

##### Challenge

Holding onto negative stories about our learning puts needless blocks and limits on what we can accomplish. Question and re-write the stories you tell yourself about who you are as a learner!

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