Basic Math Review Flashcards

Comprehensive vocabulary flashcards covering basic math principles including number types, properties, fractions, decimals, rates, simple interest, statistics, geometry, and introductory algebra.

NATURAL NUMBERS

The set of numbers starting from one: ${1, 2, 3, 4, 5, \dots}$

WHOLE NUMBERS

The set of numbers starting from zero: ${0, 1, 2, 3, 4, \dots}$

INTEGERS

The set of whole numbers and their opposites: ${\dots, -3, -2, -1, 0, 1, 2, \dots}$

RATIONAL NUMBERS

All numbers that can be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$.

IRRATIONAL NUMBERS

Real numbers that cannot be written as the quotient of two integers but can be represented on the number line.

REAL NUMBERS

Include all numbers that can be represented on the number line, comprising all rational and irrational numbers.

PRIME NUMBERS

A number greater than $1$ that has only itself and $1$ as factors, such as $2, 3,$ and $7$.

COMPOSITE NUMBERS

A number that is not prime; for example, $8$ is a composite number since $8 = 2 \times 2 \times 2 = 2^3$.

Identity Property of Zero (Addition)

$$a + 0 = a$$

Inverse Property (Addition)

$$a + (-a) = 0$$

Commutative Property (Addition)

$$a + b = b + a$$

Associative Property (Addition)

$$a + (b + c) = (a + b) + c$$

Property of Zero (Multiplication)

$$a \times 0 = 0$$

Identity Property of One (Multiplication)

$$a \times 1 = a$$

Inverse Property (Multiplication)

$a \times \frac{1}{a} = 1$, when $a \neq 0$.

Commutative Property (Multiplication)

$$a \times b = b \times a$$

Associative Property (Multiplication)

$$a \times (b \times c) = (a \times b) \times c$$

Property of Zero (Division)

$\frac{0}{a} = 0$, when $a \neq 0$. Note: Division by zero is undefined.

Property of One (Division)

$\frac{a}{a} = 1$, when $a \neq 0$.

Identity Property of One (Division)

$$\frac{a}{1} = a$$

Absolute Value

The distance of a number from zero, which is always $\ge 0$. If $a \ge 0$, $|a| = a$, and if $a < 0$, $|a| = -a$.

LEAST COMMON MULTIPLE (LCM)

The smallest number that is a multiple of all the given numbers in a set.

GREATEST COMMON FACTOR (GCF)

The largest number that can be evenly divided into each of the given numbers in a set.

Numerator

The top number of a fraction expressing division.

Denominator

The bottom number of a fraction expressing division.

Sum

The result of adding two addends ($\text{addend} + \text{addend} = \text{sum}$).

Difference

The result of subtracting a subtrahend from a minuend ($\text{minuend} - \text{subtrahend} = \text{difference}$).

Product

The result of multiplying two factors ($\text{factor} \times \text{factor} = \text{product}$).

Quotient

The result of dividing a dividend by a divisor ($\text{dividend} \div \text{divisor} = \text{quotient}$).

Mixed Number

A number composed of two parts: a whole number part and a fractional part, such as $5 \frac{3}{8}$.

Improper Fraction

A fraction where the numerator is greater than or equal to the denominator, such as $\frac{20}{3}$.

Rate

A comparison of two quantities with different units.

Ratio

A comparison of two quantities with the same units.

Proportion

A statement indicating that two ratios or rates are equal, solved using cross-multiplication.

Percent

The number of parts out of $100$.

Simple Interest Formula

$I = p \times r \times t$, where $I$ is interest, $p$ is principal, $r$ is percentage rate, and $t$ is time.

Scientific Notation

A way to express numbers in the form $a \times 10^n$, where $1 \le |a| < 10$ and $n$ is an integer.

Mean

The sum of all data values divided by the number of values; also known as the average.

Median

The middle number in an ordered list of data (or the average of the two middle numbers if the count is even).

Mode

The number (or numbers) in a list that occurs most frequently.

Distance Formula

$d = r \times t$, where $d$ is distance, $r$ is rate, and $t$ is time.

Perimeter

The distance around a geometric figure or the sum of the lengths of its sides.

Area of a Rectangle

$$A = L \times W$$

Area of a Triangle

$$A = \frac{1}{2} b \times h$$

Pythagorean Theorem

In any right triangle with legs $a$ and $b$ and hypotenuse $c$, the formula is $a^2 + b^2 = c^2$.

Variable

A letter that represents a number because the number is unknown or can change.

Constant

A term that does not change, such as the number $7$ representing days in a week.

Algebraic Expression

Consists of constants, variables, numerals, and at least one operation.

Equation

A mathematical sentence indicating that two expressions are equal.

Solution

A number that makes an equation true.