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🌍 Arithmetics · flashcards
Arithmetics Arithmetic Flashcards
50 question-and-answer cards covering Arithmetic as it is examined in Arithmetics. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Arithmetic deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
Why is $1$ neither prime nor composite?
$1$ has only one positive divisor (itself), so it fails the two-divisor requirement for primes and the more-than-two requirement for composites.
What is the only even prime number?
$2$ is the only even prime; every other even number is divisible by $2$ and thus composite.
Define a composite number.
A composite number is a natural number greater than $1$ that has more than two positive divisors — i.e., it has at least one factor other than $1$ and itself.
Is $51$ prime or composite? Justify.
Composite, because $51 = 3 \times 17$, so it has divisors beyond $1$ and itself.
What is prime factorization?
Prime factorization is expressing a composite number as a product of prime numbers, e.g. $60 = 2^{2} \times 3 \times 5$.
State the Fundamental Theorem of Arithmetic.
Every integer greater than $1$ can be written as a product of primes in exactly one way, apart from the order of the factors.
Find the prime factorization of $84$.
$84 = 2^{2} \times 3 \times 7$.
How do you find the GCD of two numbers using prime factorization?
Factor both into primes and multiply the common prime powers using the lowest exponent of each. E.g. $12 = 2^{2}\times 3$, $18 = 2\times 3^{2}$, so $\gcd = 2^{1}\times 3^{1} = 6$.
How do you find the LCM using prime factorization?
Take each prime that appears and use its highest exponent. E.g. $12 = 2^{2}\times 3$, $18 = 2\times 3^{2}$, so $\operatorname{lcm} = 2^{2}\times 3^{2} = 36$.
What is the result of adding two integers with opposite signs?
Subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value, e.g. $-7 + 3 = -4$.
What is the rule for the sign of a product/quotient of two numbers?
Same signs give a positive result; different signs give a negative result. E.g. $(-4)\times(-3)=12$ and $(-4)\times 3 = -12$.
How does subtracting a number relate to addition?
Subtracting a number equals adding its additive inverse: $a - b = a + (-b)$.
How does dividing by a fraction relate to multiplication?
Dividing by a fraction equals multiplying by its reciprocal: $a \div \frac{b}{c} = a \times \frac{c}{b}$.
Why is division by zero undefined?
$a \div 0$ asks for a number $x$ with $0 \times x = a$; for $a \neq 0$ no such $x$ exists, and for $a = 0$ every $x$ works, so it is undefined.
Is the set of integers closed under division? Give an example.
No. For example $7 \div 2 = 3.5$, which is not an integer. Integers are closed under addition, subtraction, and multiplication only.
State the standard order of operations.
Parentheses, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right) — PEMDAS.
Evaluate $2 + 3 \times 4^{2}$ using order of operations.
$4^{2} = 16$, then $3 \times 16 = 48$, then $2 + 48 = 50$.
What is a divisor (factor) of a number?
A divisor of $n$ is an integer that divides $n$ evenly, leaving remainder $0$. E.g. the divisors of $6$ are $1, 2, 3, 6$.
State the divisibility rule for $3$.
A number is divisible by $3$ if the sum of its digits is divisible by $3$. E.g. $123$: $1+2+3=6$, divisible by $3$.
State the divisibility rule for $9$.
A number is divisible by $9$ if the sum of its digits is divisible by $9$. E.g. $729$: $7+2+9=18$, divisible by $9$.
What does it mean for a number to be even or odd, in terms of divisibility?
An even number is divisible by $2$ (ends in $0,2,4,6,8$); an odd number is not divisible by $2$ (ends in $1,3,5,7,9$).
Compare the density of rationals and integers on the number line.
Integers are discrete (gaps of $1$ between them), while rationals are dense — between any two rationals there is always another rational.
Classify the number $0$ across the number systems.
$0$ is a whole number, an integer, a rational number ($\frac{0}{1}$), and a real number, but it is not a natural number (in the counting convention) and is neither prime nor composite.
What is the sum of an irrational number and a nonzero rational number?
It is always irrational. E.g. $2 + \sqrt{3}$ is irrational, because if it were rational, subtracting the rational $2$ would make $\sqrt{3}$ rational — a contradiction.
What this deck covers
The Arithmetic deck follows the Arithmetics Arithmetic syllabus — 10 chapters and 54 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 5.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 123 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Arithmetic flashcards FAQ
How many Arithmetic flashcards are in this Arithmetics deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these Arithmetics flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Arithmetic cards cover?
They follow the Arithmetics Arithmetic syllabus — 10 chapters and 54 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.