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Kiselev's Arithmetic

by A. P. Kiselev

Translated by Valery Manokhin, PhD

The foundational arithmetic textbook used in Russian schools for over a century. 6 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation.

6 chapters · 214 numbered articles · 192 pages

Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.

United States4–7Elementary math → Pre-Algebra
United KingdomYears 5–8KS2 into KS3 · pre-GCSE
CanadaOntario 4–7BC Math 4–7 · QC Elementary 4 – Secondary I

Not covered in this book

negative numbers · coordinate geometry · statistics and data handling · probability · percentages

Source these strands elsewhere. They are missing from the book, not from this description.

How this book fits

See the whole sequence →

Covers much of the same ground

These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.

What comes next

Table of contents

25 section headings — the printed contents page in full.

Translator's Preface

Section I. WHOLE NUMBERS7 sections
  1. I. Whole numbers, their naming and notation
  2. II. Various systems of numeration. Roman numerals
  3. III. Addition
  4. IV. Subtraction
  5. V. Signs of operations. Signs of equality and inequality. Brackets
  6. VI. Multiplication
  7. VII. Division
Section II. ON THE DIVISIBILITY OF NUMBERS5 sections
  1. I. Tests of divisibility
  2. II. Decomposition of numbers into prime factors
  3. III. Finding the divisors of a composite number
  4. IV. Greatest common divisor of several numbers
  5. V. Least common multiple of several numbers

Section III. MEASUREMENT OF QUANTITIES. THE METRIC SYSTEM OF MEASURES

Section IV. COMMON (SIMPLE) FRACTIONS5 sections
  1. I. Fundamental concepts
  2. II. Change in the value of a fraction with a change in its terms
  3. III. Reduction of a fraction
  4. IV. Reduction of fractions to the least common denominator
  5. V. Operations on fractional numbers
Section V. DECIMAL FRACTIONS4 sections
  1. I. Basic properties of decimal fractions
  2. II. Operations on decimal fractions
  3. III. Conversion of common fractions into decimals
  4. IV. Conversion of periodic fractions into common ones
Section VI. PROPORTIONAL QUANTITIES4 sections
  1. I. Proportions
  2. II. Proportional dependence of quantities
  3. III. Problems on proportional division
  4. Table Of Prime Numbers Not Exceeding 6000

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Formats and editions

FormatPriceISBN-13WhereBuy
PDF$44.95Gumroad · Instant downloadBuy →
Kindle$54.95AmazonBuy →
Paperback$49.95978-1-80910-038-2AmazonBuy →
Hardcover$74.95978-1-80910-039-9AmazonBuy →

Prices are the publisher list prices. Amazon sets the final price in each store.

Product details

Publisher
Northern Star Academic Press
Language
English
Translator
Valery Manokhin, PhD
Print length
192 pages
First published
2026-09-11

Published by Northern Star Academic Press · First faithful English translation from the original Russian edition

Browse the full Russian Math Classics series on Amazon →

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