arithmetic
B1Neutral to Formal
Definition
Meaning
The branch of mathematics dealing with the properties and manipulation of numbers, especially addition, subtraction, multiplication, and division.
Also used to refer to calculations in general, or to the act or process of calculating numerically.
Linguistics
Semantic Notes
As a noun, refers to the subject or process. The adjective form is often used in fixed terms like 'arithmetic mean' or 'arithmetic progression'.
Dialectal Variation
British vs American Usage
Differences
The primary difference is in the pronunciation of the noun form, specifically the stress pattern: BrE typically stresses the second syllable (/əˈrɪθ.mə.tɪk/), AmE often stresses the third syllable (/əˈrɪθ.məˌtɪk/ or /ˌær.ɪθˈmet̬.ɪk/). The adjective form is consistently stressed on the third syllable in both variants.
Connotations
Identical connotations in both varieties.
Frequency
Slightly more common in its technical/mathematical sense in academic registers. Similar overall frequency.
Vocabulary
Collocations
Grammar
Valency Patterns
N + of + arithmetic (e.g., 'the rules of arithmetic')Adj + arithmetic (e.g., 'basic arithmetic')Do/perform arithmeticVocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “Do the arithmetic (meaning: calculate the implications, often figuratively)”
Usage
Context Usage
Business
Used in financial contexts, e.g., 'The arithmetic of the proposed merger doesn't add up.'
Academic
Core term in mathematics education and number theory.
Everyday
Refers to basic calculations, e.g., checking a bill or helping a child with homework.
Technical
Specific meanings in computing (arithmetic logic unit) and mathematics (arithmetic series).
Examples
By Part of Speech
verb
British English
- N/A (rare/obsolete). 'To arithmetic' is not standard.
American English
- N/A (rare/obsolete). 'To arithmetic' is not standard.
adverb
British English
- N/A. 'Arithmetically' is the adverbial form.
American English
- N/A. 'Arithmetically' is the adverbial form.
adjective
British English
- The arithmetic mean of the dataset was calculated.
- He made an arithmetic error in his tax return.
American English
- She is studying arithmetic progression in her algebra class.
- The report contained a serious arithmetic mistake.
Examples
By CEFR Level
- Children learn arithmetic in primary school.
- I need to check the arithmetic on this receipt.
- The project's budget failed because of a simple arithmetic error.
- Good mental arithmetic is useful when shopping.
- The arithmetic of climate change suggests we need to act urgently.
- He questioned the arithmetic behind the government's economic forecast.
- The arithmetic progression formed the basis of the complex algorithm.
- One must understand the underlying arithmetic of compound interest to manage debt effectively.
Learning
Memory Aids
Mnemonic
Think: 'A RAT In The House Might Eat The Ice Cream' uses the first letters of ARITHMETIC.
Conceptual Metaphor
Arithmetic is the foundation/building block (for more complex mathematics).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with 'арифметика' (the school subject) when the English word is used in a broader figurative sense (e.g., 'political arithmetic').
Common Mistakes
- Misspelling as 'arithMatic' (confusion with 'automatic').
- Incorrect stress in speech, especially for learners using the noun form.
Practice
Quiz
Which sentence uses 'arithmetic' as an adjective?
FAQ
Frequently Asked Questions
Arithmetic is the foundational branch of mathematics dealing specifically with numbers and basic operations (+, -, ×, ÷). Mathematics is the broader field that includes arithmetic, algebra, geometry, calculus, etc.
It is usually uncountable when referring to the subject or skill (e.g., 'She is good at arithmetic'). It can be countable, though less common, when referring to a specific set of calculations (e.g., 'the arithmetics of different scenarios').
As a noun (most common), British English stresses the second syllable: uh-RITH-muh-tik. American English often stresses the third syllable: uh-rith-MET-ik. As an adjective, both varieties stress the third syllable: ar-ith-MET-ic.
Mental arithmetic refers to performing calculations in one's head, without the aid of tools like a calculator, pen, and paper. It is a valued skill for speed and estimation.
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