What is an Algebraic Expression?

Algebra is a powerful tool that lets us describe patterns, rules, and relationships using symbols instead of words. Scientists use algebra every day — to write formulas for speed, to describe how temperature changes, or to predict the outcome of an experiment. At the heart of algebra is the algebraic expression.

Algebraic Expression

A mathematical phrase made up of variables (letters), numbers, and operations (such as +, −, ×, ÷). For example: $4 y$ , $t - 10$ , $n + 2$ , and $3 w + 5$ are all algebraic expressions. Notice there is no equals sign — an expression is not an equation.

Variable

A letter that represents an unknown or changing number. Common choices are $x$ , $y$ , $a$ , $b$ , $n$ , etc. In science, we often choose letters that remind us of what they stand for — $t$ for time, $d$ for distance, $T$ for temperature.

Here are some expressions and what they mean in words:

Expression	Meaning
$x + 7$	a number plus seven
$3 m$	three times a number
$4 a - 8$	eight less than four times a number
$\frac{d}{5}$	a number divided by five
$\frac{k}{6} + 2$	two more than a number divided by six

Now let's look at the parts that make up an expression:

Term

A single number, variable, or product of numbers and variables. Terms are separated by + or − signs. In $3 a + 4$ , there are two terms: $3 a$ and $4$ .

Coefficient

The number that is multiplied by a variable in a term. In $7 x$ , the coefficient is $7$ . In $3 w + 5$ , the coefficient of $w$ is $3$ .

Constant

A number on its own in an expression — its value never changes. In $3 a + 4$ , the number $4$ is a constant.

Expression vs Equation

An expression is a mathematical phrase with no equals sign: $3 x + 5$ . An equation states that two things are equal — it always has an equals sign: $3 x + 5 = 14$ . In this unit we focus on forming and simplifying expressions.

Note

In algebra, we never write the multiplication symbol $\times$ between a number and a letter. This is because $\times$ looks too much like the letter $x$ ! Instead, we write the number directly in front of the letter: $3 w$ means $3 \times w$ .

Note

Science connection: In MYP Sciences, you will use algebraic expressions inside scientific formulas. For example, the formula for speed is $v = \frac{d}{t}$ , where $d$ is distance and $t$ is time. Understanding how expressions work is the key to using formulas confidently in experiments!

Algebra in Scientific Formulas

In MYP Sciences, algebra is most commonly used when working with scientific formulas — rules that connect measurable quantities. Every time you use a formula in an experiment, you are working with algebraic expressions.

Here are some common science formulas you will encounter:

Formula	What it means
$v = \frac{d}{t}$	speed = distance ÷ time
$D = \frac{m}{V}$	density = mass ÷ volume
$W = m g$	weight = mass × gravitational field strength
$P = \frac{F}{A}$	pressure = force ÷ area

Note

Notice that scientific formulas use their own established letter choices — $v$ for speed (velocity), $m$ for mass, $g$ for gravitational field strength. These letters are chosen because they are standard in science, not because of alphabetical order. Scientific convention takes priority over alphabetical ordering!

Independent and dependent variables in science

Independent Variable

The variable you change deliberately in an experiment. In an expression or formula, this is the letter whose value you choose to substitute in.

Dependent Variable

The variable you measure as a result. This is the quantity the formula calculates for you after you substitute the independent variable.

Example

Speed formula: $v = \frac{d}{t}$

If you are investigating how speed changes as time increases:

Independent variable: $t$ (time — you control this)
Dependent variable: $v$ (speed — you calculate this)

If distance $d = 60$ m and time $t = 5$ s:
$v = \frac{60}{5} = 12 m/s$

✅ Notice we always include units (metres per second, m/s) in scientific calculations!

Exam Tip

When substituting into a scientific formula, always:

Write the formula
Substitute the numbers (with units)
Calculate the answer
State the units in your final answer

Units are not optional in science — a speed of "12" means nothing; "12 m/s" tells you something useful!

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