GRE Arithmetic Flashcards

Flashcards for GRE Arithmetic Review

Real Numbers

All numbers on the number line; all the numbers on the GRE are real.

Rational Numbers

All numbers that can be expressed as the ratio of two integers (all integers and fractions).

Irrational Numbers

All real numbers that are not rational, both positive and negative (e.g., π, √3).

Integers

All numbers, including zero, with no fractional or decimal parts.

PEMDAS

Please Excuse My Dear Aunt Sally - This mnemonic will help you remember the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Commutative Law

Addition and multiplication are both commutative; it doesn't matter in what order the operation is performed (e.g., 5 + 8 = 8 + 5; 2 x 6 = 6 x 2).

Associative Law

Addition and multiplication are also associative; the terms can be regrouped without changing the result [e.g., (a + b) + c = a + (b + c); (a x b) x c = a x (b x c)].

Distributive Law

The distributive law of multiplication allows us to distribute a factor among the terms being added or subtracted. In general, a(b + c) = ab + ac.

Equivalent Fractions

The value of a fraction is unchanged if you multiply the numerator and denominator by the same nonzero number.

Reducing Fractions

To put a fraction in lowest terms, divide out any common multiples from both the numerator and denominator.

Common Denominator

A common multiple of the denominators of fractions; necessary for addition and subtraction.

Least Common Denominator (LCD)

The least common multiple of the denominators of fractions.

Reciprocal

To get the reciprocal of a fraction, invert it by interchanging the numerator and the denominator.

Complex Fraction

A fraction that contains one or more fractions in its numerator or denominator.

Mixed Numbers

Numbers consisting of an integer and a fraction (e.g., 3 1/2, 1 1/4, 5 3/8).

Decimal Fractions

Another way of expressing common fractions; they can be converted to common fractions with a power of ten in the denominator.