**WORD FRACTION TECHNIQUE**

WHY AND HOW IT WORKS

WHY AND HOW IT WORKS

It is a fact that most students find difficulty with word problems because they cannot convert the problem’s words into

the correct equation. Generally, finding an equation is the last thing they are considering. They typically are rushing to

do some math operation on the given numbers, which sadly, is usually the incorrect operation. There are a lot of

reasons for this, none of which will be discussed herein.

**is a totally different technique designed to provide a universally applicable**

__The Word/Fraction Technique (W/F)__method to directly convert the words and the associated data into an equation by an easily understood method.

A Word/Fraction is defined as any fraction containing dimensions only or number and dimensions

**feet/feet 3 feet/yard 60 miles/hour $8.75/hour 10 pounds / $2**

The basic theorem of W/F is that W/F may be inverted as needed if they equal ‘1’

**60 miles/ hour = hour/ 60 miles $2 / 10 pounds = 10 pounds / $2**

As with virtually all, the above W/F equal ‘1’ as long as the dimensions are retained together with numerical values

The first basic ‘commandment’ of W/F is :

**NO MATH OPERATIONS BEFORE DEVELOPING AN EQUATION !**

Quite a difficult job ? Absolutely, without question, YES … but read on !!

W/F is an extension of a recognized tool in Science and Engineering Universities: Dimensional Analysis. (DA) .

Simply stated, DA postulates that all dimension units on the left of a valid equation must equal all dimension units

on the right side. In practice, the right side is only the ‘answer to the problem’ both numerically and dimensionally

(e.g. 60 miles per hour or $5.23 or 24 students)

Initially, most equations being generated will contain many dimensional units on the left side other than, but always

including, the answer’s dimensional units. BUT.. here’s the payoff of DA:

**If all units, other than the answer’s units, can be canceled by a common numerator and denominator then the equation**

is dimensionally balanced provided the remaining answer names on either side of the equation have identical numerator and denominator

is dimensionally balanced provided the remaining answer names on either side of the equation have identical numerator and denominator

**positions.**

So, the basic concept of W/F is : The student creates an initial equation using all the given data

**without regard to its**

**correctness !!!.**Using DA, he corrects the equation as needed by inverting W/F and/or adding his own ‘equal to ‘1’

W/F until the equation becomes dimensionally balanced. (see below for a step by step solution of a real problem)

__W/F needs to first train the student in basic math concepts applicable to math word problems, for example:__**Any 'thing’ multiplied or divided by ‘1’ results in the same value as the original value**

**You may only add or subtract the values of like items**

**You may multiply or divide the values of like or unlike items**

**Any 'thing’ divided by itself or (something equivalent to it ) = 1**

**2 dogs = 2 x dogs 24 feet / 3 seconds = 8 feet /sec.**

**There is no difference between singular vs. plural version of the unit**

dimension name ( feet = foot miles = mile)

dimension name ( feet = foot miles = mile)

**Provide a list of non-math common words that have real mathematically meaning**

(e.g. is, what, of, per, a, %, by, etc.)

(e.g. is, what, of, per, a, %, by, etc.)

**:**

__Using the W/F technique__**: What is the unit name of the answer ? Write an ’= ? ’ followed by the units of the answer**

__Step 1__(which is given in the problem usually after ‘How many .....‘ or 'What %...' , etc.) such as:

**= ? $ = ? $ / lb. = ? students = ? % = ? Cm ^2 (square)**

**Check if there are any duplicate W/F with different values included. If so, show them inside a parenthesis**

__Step 2:__and either add or subtract).

**On the left side off the equation multiply all W/F with unique dimensions.**

__Step 3:__**Cancel any pair of identical numerators and denominators.**

__Step 4:__**: If still unbalanced, add ‘conversion’ W/F (e.g. 12 inches/foot or foot/12 inches) in order to cancel**

__Step 5__any ‘non-answer’ dimensions that remain.

**Finally , once only answer names (in proper NUM/DEN position) appear in the left side, perform the indicated operations.**

__Step 6:__**Note that this procedure**

__automatically__handles the issue of whether to**multiply or divide and if so, what elements**

**. (A major problem with many students !)**

**Try the following 'SIMPLE' problem: (IF YOU ARE A TEACHER ,**

**TEST YOUR MATH CLASS...**

**WITHOUT USING THE WORD/FRACTION TECHNIQUE ....**

**CARE TO GUESS AN ESTIMATE FOR THE '% CORRECT**'

**MY TAPE RECORDER RUNS AT A SPEED OF 7 1/2 INCHES PER SECOND. HOW MANY HOURS**

**CAN A 1800 FOOT ROLL OF TAPE BE PLAYED ?**