Ray's Arithmetic · Book 3 · 1877
Written arithmetic for children about 9 to 12: place value, the four operations, money and measures, fractions, decimals and percentage, with rules, worked examples and hundreds of problems. Every session has a guide you can follow step by step, with the right page of the book beside it.
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Units, figures and place value; writing and reading large numbers; Roman numerals. Lessons 1–6.
Adding columns of numbers with carrying, proving the sum, and story problems. Lessons 7–10.
Taking away, borrowing, proving by addition, and mixed problems. Lessons 11–13.
Multiplying by one figure and by many, proving the product, and short cuts. Lessons 14–18.
Short and long division, short cuts, and the principles behind division. Lessons 19–25.
Compound numbers, reading and writing dollars, cents and mills, and the four rules with money. Lessons 26–32.
Dry and liquid measure, weight, length, area, volume and time, and how to change from one unit to another. Lessons 33–40.
Adding, subtracting, multiplying and dividing measures of mixed units; time between dates; longitude and time. Lessons 41–46.
Prime numbers, prime factors, greatest common divisor, least common multiple, and cancellation. Lessons 47–51.
What fractions are, reducing them, and adding, subtracting, multiplying and dividing them, with measures and money. Lessons 52–62.
Decimal places, writing and reading decimals (the rest of decimals is in the next part of the book). Lessons 63–64.
Change decimals to fractions and back, then add, subtract, multiply and divide them, and use them with measures and money. Lessons 65–72.
Meters, ars, liters and grams, and how they compared with the old American measures in 1877. Lessons 73–75.
Per cent as hundredths, and the four cases of base, rate and percentage. Lessons 76–79.
Commission, trade discount, and profit and loss, the way 1870s merchants worked them. Lessons 80–82.
Shares, bonds, brokerage, dividends, premiums and discounts, and the income from an investment. Lessons 83–84.
Simple interest in all its cases, the 12 per cent shortcut, compound and annual interest, and partial payments. Lessons 85–92.
Bank discount, notes, days of grace, and true discount (present worth). Lessons 93–95.
Paying distant debts with drafts, at home and abroad, with English, French and German money. Lessons 96–97.
Fire, marine and life insurance premiums. Lessons 98–98.
Property and poll taxes, tax tables, internal revenue and customs duties. Lessons 99–100.
Ratios as quotients, then simple and compound proportion (the old "Rule of Three"). Lessons 101–105.
Sharing gains and losses in proportion, average due dates, and mixtures. Lessons 106–108.
Powers, square roots and cube roots by hand, with the square-and-strips picture that explains them. Lessons 109–114.
Areas of flat figures, surfaces and volumes of solids, and how tradesmen measured their work. Lessons 115–120.
Arithmetical and geometrical series: last terms, differences and sums. Lessons 121–122.
Working on paper: long multiplication and division, fractions, decimals, measures, percentage and interest. The core book of the series.
Scanned from a University of California copy. (Printed pages 39–42 are missing from this scan.)
The book is divided into numbered articles, not lessons. Each guide covers a few articles, shown beside its title. The guides are written for this site; the book is in the public domain.