Table of Contents

Page

Introduction

Adding and Subtracting Fractions

Adding Fractions with Denominators

that are not Relatively Prime

Adding Three Fractions with Three

Different Denominators

What about Mixed Numbers?

Some Practice Exercises

 

 Fractions, demons, monsters too,

All these things they are to me,

And when I try to add them so,

They daunt me, flaunt me blow by blow.

Denominators must be true,

To stay no need now I must flee.

To get agreement though I try,

These demons make me want to cry.

So teach me how to reckon two,

The method straight, I want to see,

My mind is set, my spirit won,

To slay these demons one by one.

 

Introduction

Fractions. Ugh! I could just hear the squeals coming from my students any time we

entered the realm of these nasty little demons. Anytime we embarked on an area of mathematics

that would require heavy fraction work, students would act as though we were entering Hades

after an arduous crossing of the river Acheron, led by the fearless ferry-man Charon and his

threeheaded dog Cerberus. Ouch! It was that bad.

Indeed, of all the pain-causing topics in elementary mathematics, fractions by far have to

be the one that ranks highest on a student.s scale of misery-makers. Students are barely making

ends meet with the whole numbers and integers when suddenly these strange monsters called

fractions are introduced on the scene. And even though the ancient Greeks gave them the name

rational numbers because they thought these numbers were quite sane compared to the insane

irrational numbers like pi (you know the number equal to about 3.14), the fractions do nothing but

drive those students, who endeavor to study them, quite insane.
 

Yet in all reality, these nuisances we call fractions are not nearly so demonic as they are

made out to be. And when we consider how important they are in the study of all areas of

mathematics, we best give them their proper place.and respect. At the early ages, children

stumble over these entities because they are inherently difficult to reckon with. Unlike whole

numbers, which consist of one part, fractions (or rationals, as they are called) consist of two: the

numerator, or top part, and the denominator, or bottom part. Pretty much everyone knows this.

And these monsters are quite friendly when we perform the arithmetic operations of multiplication or

division. However, add or subtract.now we.re talking serious business. Students would cringe at the

thought of adding two fractions with unusually different denominators, not to mention three fractions

with different bottoms. I guess .bottoms up. would not apply here.

Why are fractions so hard? Well maybe it has something to do with their intrinsic makeup.

You see, the counting numbers have only one part to them. That is, numbers like 1, 2, or 5 are

what you see is what you get.. But fractions, not content with one part, have two: the

numerator, or top part, and the denominator, or bottom part. And here.s where the problem lies:

for the denominator puts each fraction into its own unique class. To understand the nature of this

problem, consider the following: when a student needs to add two whole numbers, such as 5 and

3, the calculation can be done immediately to get the sum of 8. However, if the student wishes to

add the two fractions 1/5 and 1/8, the calculation cannot be done so quickly as the whole number

example. The reason is that the two fractions have different denominators. This is what puts

fractions on a different playing field than the whole numbers. This two-part, or dual nature of

fractions is what sets them apart from other numbers. In fact, this very nature is what makes the

set of fractions (which happens to be an infinite set like the set of whole numbers) a peculiarly

interesting bunch of characters.
 

You see the denominator by being on the bottom makes the fraction a difficult creature to

work with. If you want to add two fractions like 1/3 and ½, you cannot just add the numerators

to get 2 and the denominators to get 5. This type of voodoo arithmetic has no basis in reality here

in this realm of numbers. The different denominators will not permit this. What you have to do is

first get these two fractions on a level playing field, and that.s where the concept of a least

common denominator or LCD, comes into play.

 
Once the fractions have been converted into ones with the same denominator, they are

easily managed and become like tame pussycats. Until we get to this step, however, they can be

like raging tigers, ready to rip the flesh of your test grades and wreak havoc on your math grades.

One slip-up with a fraction, and out comes the teacher.s red ink and down goes the test grade.

At any rate, truth be told: arithmetic operations with fractions are not difficult.even the

operation of addition and subtraction, which require an LCD before the operation can be

performed.
 

To follow, I will teach some powerful, easy-to-learn methods of dealing with these

dreaded demons. My focus will be on adding and subtracting fractions, as these are the difficult

operations. Once learned, you will be slaying these behemoths and reversing roles on them: You

will be the victor and fractions will be the losers, time and again. Enjoy the ride.

Click to Return to Fractions for the Faint of Heart