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N SOME books on arithmetic percentage is treated as if it were a special process involving certain distinctive principles, and therefore entitled to rank as a separate department. This elaborate treatment seems to be a mistake on both the theoretical and the practical side. growth of number as measurement, percentage presents nothing new. -The Psychology of Number.
THE pupil having learned the meaning and use of the term per cent, should find very little difficulty in the subject of interest. However, in the problems of interest and kindred commercial work, pupils frequently fail; but if the cause of the failure is examined into, it will nearly always be found to be, not so much an inability to meet the mathematics of the problems as a want of accurate knowledge of the terms used, and of acquaintance with the business forms and operations involved. On this account, in taking up the applications of arithmetic to commercial work, the teacher should be at great pains to ensure that every pupil understands well, and sees clearly through all such forms and operations.
-The Psychology of Number,
By MCLELLAN AND DEWEY.
Percentage, like many other things in arithmetic, is not difficult if the child is given a natural and simple introduction to it. Informally, it may be connected with the child's work in fractions in such a way that at no stage of the study will he fear it and call it "hard."
The manner of presenting given here is one way. The original teacher may have as good, or even a better way.
DEVELOPING THE IDEA.
Present in this way:-If anything is divided into a hundred parts, each part is called one hundredth. Three parts are called three hundredths; four parts are called- ? six parts? twenty parts .? How many hundredths in all of a thing?
(Illustrate all of the above, if the child's previous
work does not enable him to grasp it readily.)
Well, we are going to give all of a thing a new
name and call it 100 per cent.
1 hundredth of it, we will call 1 per cent.
4 hundredths of it, we will call 4 per cent.
10 hundredths of it, we will call 10 per cent, etc. 25 hundredths are
per cent ?
50 hundredths are
per cent ?
PER CENT means HUNDREDTHS.
Since per cent means hundredths,
0% of it.
75% of it.
50 per cent of a number is 5% of it.
100% = # So any per cent of a number may be written as hundredths and often can be reduced to a fraction with a small denominator.
Since per cent means hundredths, we may write any fraction whose denominator is 100 as so many per cent, as,
16 per cent.
100 25 per cent.
Write other fractions whose denominators are 100 as per cent.
THE SIGN %.
When we wish to write per cent quickly, we use this sign, %, which is always read "per cent." 7% is read "7 per cent." 10% is read "10 per cent."
We will use this sign hereafter in most cases.
TO REMOVE THE SIGN %.
To write a rate per cent as a common fraction,
1. Write the number of per cent for the numerator and 100 for the denominator.
2. Reduce the fraction to lowest terms.
Observe this illustrated in the table that follows:
Table of Values.
The pupil knows how to write any fraction, whose denominator is 10 or a multiple of 10, as a decimal