Mathematics Fundamentals: Numbers, Algebra, and Linear Relationships

Comprehensive vocabulary flashcards covering basic number properties, divisors, number planes, linear equations, algebraic techniques, and percentages based on lecture notes.

Composite number

A number that has more than two factors and is not prime.

Multiples

Numbers generated by multiplying a base number by integers; for example, multiples of $20$ include $20, 40, 60, 80, \text{...}$

Lowest common multiple (LCM)

The smallest multiple shared by $2$ or more numbers; for example, the LCM of $20$ and $15$ is $60$.

Factors

Numbers that can be multiplied together to get another number; for example, factors of $20$ are $1, 2, 4, 5, 10, 20$.

Highest common factor (HCF)

The largest factor that is shared between two or more numbers; for example, the HCF of $20$ and $15$ is $5$, and the HCF of $6$ and $8$ is $2$.

Base

The number in index notation that is being multiplied by itself; in $3^5$, $3$ is the base.

Index

Also known as the power; it indicates how many times the base is multiplied by itself. In $3^5$, $5$ is the index.

Prime number

A number that only has two factors: $1$ and itself (e.g., $5$ and $17$). Note that $1$ is not a prime number.

Square numbers

Numbers resulting from a number multiplied by itself; the first 10 are $1, 4, 9, 16, 25, 36, 49, 64, 81, 100$.

Square roots

A value that, when multiplied by itself, gives the original number; for example, \text{\textsurd} 16 = 4 and \text{\textsurd} 25 = 5.

Dividend

The number being divided in a division problem; for example, in 52 \textdiv 3, $52$ is the dividend.

Divisor

The number by which the dividend is divided; for example, in 52 \textdiv 3, $3$ is the divisor.

Quotient

The result obtained from dividing one number by another (excluding the remainder).

Remainder

The amount left over after a division is complete; in the equation $52 = 3 \times 17 + 1$, the remainder is $1$.

Ordered pair

A pair of coordinates $(x, y)$ used to locate a point on the number plane, where $x$ is the across coordinate and $y$ is the up/down coordinate.

Origin

The central point on a number plane with the coordinates $(0, 0)$.

Variable term

A part of an algebraic equation that contains a variable; in $y = 2x + 1$, $2x$ is the variable term.

Constant term

A term in an algebraic expression that is a fixed number; in $y = 2x + 1$, $1$ is the constant term.

Coefficient

The number that is multiplied by a variable; in $2x + 1$, $2$ is the coefficient of $x$.

Horizontal lines

Lines on a number plane represented by the equation $y = c$, where $c$ is a constant.

Vertical lines

Lines on a number plane represented by the equation $x = c$, where $c$ is a constant.

Distributive law

A mathematical property that allows you to multiply a number by splitting it into two parts; e.g., $24 \times 12 = 24 \times (10 + 2) = 24 \times 10 + 24 \times 2$.

Variable

A letter or symbol used to represent an unknown value in algebra, such as $x$, $y$, or $k$.

Substitution

The process of replacing a variable with a specific number to evaluate an expression; e.g., if $a = 3$ and $b = -2$, then $4a - 5b = 4 \times 3 - 5 \times (-2) = 22$.

Like terms

Terms in an algebraic expression that have the same variables and can be added or subtracted together, such as $6m$ and $3m$.

Percentage

A proportion expressed as a part out of $100$; calculated as (\text{amount} / \text{whole amount}) \times 100 \text{%}.