Kiselev's Arithmetic
by A. P. Kiselev
Translated by Valery Manokhin, PhD
The foundational arithmetic textbook used in Russian schools for over a century, in complete English translation. 6 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation. Paperback, hardcover and Kindle on Amazon; the digital edition is read online in Gumroad; there is no file to download.
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.
Where this fits in school
Not sure this is the right first book? Start here →Full curriculum table — every book by school year →| United States | 4–7 | Elementary math → Pre-Algebra |
|---|---|---|
| England | Years 5–8 | KS2 into KS3 · pre-GCSE |
| Canada (Ontario) | Ontario 4–7 | BC 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
- Malinin & Burenin$44.95
- Rashevsky's Arithmetic$39.95
Rashevsky's is the short course — 95 pages, nine sections — written as a refresher rather than a first course, and it ends with plans, diagrams and graphs, which this book does not treat.
These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.
Problems to work alongside it
- Rachinsky Solutions$39.95
What comes next
- Kiselev's Algebra I$44.95
Table of contents
25 section headings — the printed contents page in full.
Translator's Preface
Section I. WHOLE NUMBERS7 sections
- I. Whole numbers, their naming and notation
- II. Various systems of numeration. Roman numerals
- III. Addition
- IV. Subtraction
- V. Signs of operations. Signs of equality and inequality. Brackets
- VI. Multiplication
- VII. Division
Section II. ON THE DIVISIBILITY OF NUMBERS5 sections
- I. Tests of divisibility
- II. Decomposition of numbers into prime factors
- III. Finding the divisors of a composite number
- IV. Greatest common divisor of several numbers
- V. Least common multiple of several numbers
Section III. MEASUREMENT OF QUANTITIES. THE METRIC SYSTEM OF MEASURES
Section IV. COMMON (SIMPLE) FRACTIONS5 sections
- I. Fundamental concepts
- II. Change in the value of a fraction with a change in its terms
- III. Reduction of a fraction
- IV. Reduction of fractions to the least common denominator
- V. Operations on fractional numbers
Section V. DECIMAL FRACTIONS4 sections
- I. Basic properties of decimal fractions
- II. Operations on decimal fractions
- III. Conversion of common fractions into decimals
- IV. Conversion of periodic fractions into common ones
Section VI. PROPORTIONAL QUANTITIES4 sections
- I. Proportions
- II. Proportional dependence of quantities
- III. Problems on proportional division
- Table Of Prime Numbers Not Exceeding 6000
Formats and editions
| Format | List price (USD) | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Digital edition | $44.95 | — | Gumroad · Read online | Buy → |
| Kindle | $54.95 | — | Amazon | Buy → |
| Paperback | $49.95 | 978-1-80910-038-2 | Amazon | Buy → |
| Hardcover | $74.95 | 978-1-80910-039-9 | Amazon | Buy → |
List price: the US publisher list price in USD, shown for reference. Amazon sets its own price in each store — see the current price on Amazon. The Gumroad price is the price charged.
The digital edition is read online in the Gumroad reader. It is not a downloadable file.
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
More in This Series
Kiselev's Algebra I
by A. P. Kiselev
US grades 7–9 · UK Years 8–10
6 chapters, 126 sections, 239 exercises. From relative numbers and polynomials through first-degree equations, powers, roots, and quadratics.
Kiselev's Algebra II
by A. P. Kiselev
US grades 9–12 · UK Years 10–13
12 chapters plus Supplements, 187 sections. Functions, quadratic systems, inequalities, logarithms, progressions, complex numbers, the binomial theorem, and continued fractions.
Kiselev's Algebra Problems
by A. P. Kiselev
US grades 7–11 · UK Years 8–12
The companion problem collection to Kiselev's Algebra. Hundreds of carefully sequenced problems and exercises that mirror the chapter structure of Algebra Part I and Part II — the same problem set Russian students worked through alongside Kiselev's algebra textbooks for over a century.