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PREFACE.

Math 67

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THE NEW AMERICAN ARITHMETIC, Part Third, is designed
for the use of those who have completed Part Second of the
series, or some similar work.

It begins, therefore, with Denominate Fractions, and thus
reviews the closing topics in the preceding volume, Decimals
and Denominate Numbers.

Percentage and its various applications, Profit and Loss,
Commission, Brokerage, Insurance, Interest, Stocks, Partial
Payments, Banking, and Investments, all of which are of
special value in qualifying pupils for mercantile business, are
treated fully and practically.

Ratio, Proportion, Partnership, Equation of Payments, and
Averaging of Accounts, are grouped together, as having much
in common in their mode of treatment.

A short chapter of problems in Analysis is given, and
Involution and Evolution are next explained, preparatory to
the article on Mensuration, in which much information of a
practical character is embodied.

The subjects thus presented complete the topics of the
greatest importance to pupils, and as much of the science of
arithmetic as is usually taught in our common schools.

Such other subjects as are generally found in higher arith-
metics are then treated, for the benefit of those who have
time to devote to these branches.

S. M.
G. M. S.

PHILADELPHIA, 1877.

Copyright, 1877, by J. H. BUTLER & Co.

ELECTROTYPED BY MACKELLAR, SMITHS & JORDAN, PHILADELPHIA.

SHERMAN & Co.PRS PHILA

THE

NEW AMERICAN ARITHMETIC.

PART III.

DENOMINATE FRACTIONS.

A Denominate Fraction is a fraction applied to a denomination; as, £12, is gal., .015 of a mile.

Note. In all examples where the word fraction is used, common fraction is meant.

CASE I. To reduce a denominate fraction to an equivalent

fraction of a lower denomination.

ORAL EXERCISES. 1. Reduce 16 qt. to the fraction of a pint. ANALYSIS.—In one quart there are 2 pints, and in 3 qt. there are 8 times 2 pints=fo or pt.

2. Reduce .3 qt. to the decimal of a pint.

ANALYSIS.—In one quart there are 2 pints, and in 3 qt. there are .3 times 2 pints = .6 pt.

8. What fraction of a peck is of a bushel? 4. What decimal of a peck is .06 of a bushel ? 5. Reduce of a drachm to the fraction of a grain. 6. Reduce .05 of a drachm to the decimal of a grain. 79. What decimal of a day is .08 of a week? 8. * of a foot is what fraction of an inch?

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