CHAPTER 4
WORD / FRACTION TECHNIQUE
Word fractions (‘W/F’) are simply fractions which contain words only or word and numbers combined.
They follow most of the rules discussed in earlier chapters.
The key points about ‘W/F’ are:
(1) You may invert them at will provided they meet certain conditions.
(2) Words may be canceled in NUM. / DEN. pairs if the word appears by
itself (‘dog’ or 'dogs') or in combination with a number (‘2 dogs’).
Remember that per Rule #12: '2 dogs' = '2 x dogs' !
Usually, ‘W/F’ are used in the normal sentences of word problems. Therefore, you must be able to recognize
them when reading. We know that a ‘W/F’ is one term divided by another. However, you will never see a problem
written as :
GASOLINE COSTS $3.30 DIVIDED BY GALLON.
Instead, the sentence would read:
GASOLINE COSTS $3.30 PER GALLON.
Is it true that ‘PER’ means ‘divided by’ ? YES ! In fact, there are a number of common words
or phrases that also mean ‘divided by’ ......
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RULE #35 WHENEVER A WORD PROBLEM STATES THAT AN ITEM CAN BE
‘TRADED’ FOR ANOTHER, THEN THE ‘W/F’ MAY BE INVERTED.
EXAMPLES
12 miles = gallon $ 6 = doz. 12 in. = ft.
gallon 12 miles doz. $6 ft. 12 in.
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What is the purpose of the ‘W/F’ technique ? Why all the emphasis of ‘W/F’ equal to ‘1’ or ‘trade’ ‘W/F’ ?
The purpose is to eliminate the guesswork on the part of the student as to whether any particular set of numbers
are to multiplied, divided, etc. Let’s try a simple problem:
MY CAR GETS 25 MILES PER GALLON. IF GASOLINE COSTS
$3.60 PER GALLON, WHAT WILL IT COST TO DRIVE 120 MILES ?
What numbers do I multiply ? What numbers do I divide ? Why ?
For most students (especially those that do not drive a car), these are very difficult questions to answer.
‘W/F’ technique always answers them correctly and automatically using built-in logic !!!
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Click for answers: PROBLEMS
1. An old movie camera (using film) runs at 20 frames a second. If there are 4 frames to the inch,
how many minutes can I get with an 80 foot roll of film ?
2. At a race way, each lap is 1 1/2 miles long. If a car runs at 120 miles per hour, how long will it take
to run 500 laps ?
3. If I save $1.50 per week in the school bank, how many years will it take me to save $195 ?
4. Each child in a family drinks 3 cups of milk per day. If there are 4 cups in a quart, and there are
4 children, how many quarts of milk should Mother buy to last 3 days ?
5. I am going to make a mosaic tile tray that will be 8 inches long and 8 inches wide
using tiles that are 1 inch by 1 inch and cost 2 cents each. What will the tiles cost me?
WORD / FRACTION TECHNIQUE
Word fractions (‘W/F’) are simply fractions which contain words only or word and numbers combined.
They follow most of the rules discussed in earlier chapters.
The key points about ‘W/F’ are:
(1) You may invert them at will provided they meet certain conditions.
(2) Words may be canceled in NUM. / DEN. pairs if the word appears by
itself (‘dog’ or 'dogs') or in combination with a number (‘2 dogs’).
Remember that per Rule #12: '2 dogs' = '2 x dogs' !
Usually, ‘W/F’ are used in the normal sentences of word problems. Therefore, you must be able to recognize
them when reading. We know that a ‘W/F’ is one term divided by another. However, you will never see a problem
written as :
GASOLINE COSTS $3.30 DIVIDED BY GALLON.
Instead, the sentence would read:
GASOLINE COSTS $3.30 PER GALLON.
Is it true that ‘PER’ means ‘divided by’ ? YES ! In fact, there are a number of common words
or phrases that also mean ‘divided by’ ......
-----------------------------------------------------------------------------------------------------------------------------
RULE #35 WHENEVER A WORD PROBLEM STATES THAT AN ITEM CAN BE
‘TRADED’ FOR ANOTHER, THEN THE ‘W/F’ MAY BE INVERTED.
EXAMPLES
12 miles = gallon $ 6 = doz. 12 in. = ft.
gallon 12 miles doz. $6 ft. 12 in.
------------------------------------------------------------------------------------------------------
What is the purpose of the ‘W/F’ technique ? Why all the emphasis of ‘W/F’ equal to ‘1’ or ‘trade’ ‘W/F’ ?
The purpose is to eliminate the guesswork on the part of the student as to whether any particular set of numbers
are to multiplied, divided, etc. Let’s try a simple problem:
MY CAR GETS 25 MILES PER GALLON. IF GASOLINE COSTS
$3.60 PER GALLON, WHAT WILL IT COST TO DRIVE 120 MILES ?
What numbers do I multiply ? What numbers do I divide ? Why ?
For most students (especially those that do not drive a car), these are very difficult questions to answer.
‘W/F’ technique always answers them correctly and automatically using built-in logic !!!
------------------------------------------------------------------------------------------------------------------------------------------------------------
Click for answers: PROBLEMS
1. An old movie camera (using film) runs at 20 frames a second. If there are 4 frames to the inch,
how many minutes can I get with an 80 foot roll of film ?
2. At a race way, each lap is 1 1/2 miles long. If a car runs at 120 miles per hour, how long will it take
to run 500 laps ?
3. If I save $1.50 per week in the school bank, how many years will it take me to save $195 ?
4. Each child in a family drinks 3 cups of milk per day. If there are 4 cups in a quart, and there are
4 children, how many quarts of milk should Mother buy to last 3 days ?
5. I am going to make a mosaic tile tray that will be 8 inches long and 8 inches wide
using tiles that are 1 inch by 1 inch and cost 2 cents each. What will the tiles cost me?