Introduction to Algebra - Practise Flashcards

These vocabulary flashcards cover the fundamental terms and concepts of algebra as presented in the lecture notes, including expressions, terms, indexing, laws of arithmetic, and algebraic fractions.

Pronumeral

A letter that can represent one or more numbers.

Variable

A word used to describe a letter that represents an unknown value or quantity.

Expression

A combination of numbers and pronumerals combined with mathematical operations, such as $3x + 2yz$.

Term

A part of an expression consisting only of pronumerals, numbers, multiplication, and division; for example, $9$, $10d$, and $\frac{x}{5}$.

Coefficient

The number in front of a pronumeral; if the term is subtracted, it is negative, and if there is no number shown, it is $1$.

Constant term

A term that does not contain any variables.

Sum

The result of addition; the sum of $a$ and $b$ is $a + b$.

Difference

The result of subtraction; the difference of $a$ and $b$ is $a - b$.

Product

The result of multiplication; the product of $a$ and $b$ is $a \times b$.

Quotient

The result of division; the quotient of $a$ and $b$ is $a \div b$.

Square of a

Represented algebraically as $a^2$.

Substitution (Evaluation)

The process of replacing each pronumeral in an expression with a number to obtain a final value.

Equivalent expressions

Expressions that always give the same result when a number is substituted for each pronumeral, regardless of the value.

Commutative laws

Arithmetic laws stating that $a + b = b + a$ and $a \times b = b \times a$ for all values of $a$ and $b$.

Associative laws

Arithmetic laws stating that $a + (b + c) = (a + b) + c$ and $a \times (b \times c) = (a \times b) \times c$ for all values of $a$, $b$, and $c$.

Like terms

Terms that contain exactly the same pronumerals with the same powers, though not necessarily in the same order.

Algebraic fraction

An expression involving division that could include any algebraic expression in the numerator or the denominator.

Lowest common denominator (LCD)

The smallest multiple of the denominators of two algebraic fractions.

Reciprocal

Formed by swapping the numerator and denominator of an algebraic fraction.

Distributive law

A law used to rewrite an expression without brackets, such as $a(b + c) = ab + ac$.

Factorising

The reverse procedure of expanding, which aims to write expressions as the product of two or more factors.

Highest common factor (HCF)

The largest factor that divides into each term in a set of terms.

Base

The number or pronumeral in index notation that is being repeatedly multiplied by itself.

Index (Exponent)

The small number in index notation (e.g., the $n$ in $a^n$) that indicates how many copies of the base are multiplied together.

Expanded form

Writing a term involving indices using repeated multiplication, such as writing $4x^3$ as $4 \times x \times x \times x$.

Index law for multiplying powers

Rule stating that when multiplying powers with the same base, you add the indices: $a^m \times a^n = a^{m+n}$.

Index law for dividing powers

Rule stating that when dividing powers with the same base, you subtract the indices: $a^m \div a^n = a^{m-n}$.