8.1 Algebraic notation and vocabulary — Learn

Prerequisites: multiplication, addition and the use of letters to stand for numbers.

By the end of this section you can: use algebraic notation and identify variables, terms, coefficients, constants, expressions, equations, identities and formulae.

Covers: A1, A3.

Learn the method

A variable is a letter that stands for a number. A term is a number, a letter, or numbers and letters multiplied together.

A coefficient is the number multiplying a variable. In $7x$, the coefficient is $7$. A constant has no variable.

An expression combines numbers, variables and operations. An equation says that two expressions are equal. An identity is true for every allowed value.

The expression $3a+5$ has two terms: $3a$ and $5$. Its coefficient is $3$, and its constant is $5$.

An inequality compares two expressions using a symbol such as $<$ or $\geq$. A factor is an expression multiplied by another expression. In $3(x+2)$, the factors are $3$ and $(x+2)$.

A formula is a rule written with symbols, such as $P=2l+2w$. It links quantities.

Worked example. Describe $7m-4$.

It is an expression, not an equation, because it has no equals sign.

Its terms are $7m$ and $-4$.

The coefficient of $m$ is $7$, and the constant term is $-4$.

Watch out. An equation is not always an identity. The equation $x+2=5$ is true only when $x=3$. The equation $x+2=2+x$ is true for every value of $x$. Check whether it holds for every value.

You should now be able to

• use algebraic notation and identify variables, terms, coefficients, constants, expressions, equations, identities and formulae.