Arithmetic Expressions – Reading and Writing Maths
An arithmetic expression is a combination of numbers and operations that represents a value. Unlike an equation, an expression does not have an equals sign.
Learning to move fluently between plain-language descriptions and symbolic expressions is a skill every programming language relies on too — when a spreadsheet formula reads =3*A1+7 or a line of code reads total = 3 * price + 7, both are just arithmetic expressions written in a stricter, machine-readable dialect of the same algebraic language covered here. This is exactly why the ability to translate “three less than a quarter of x” into x/4 − 3 is not just a maths-class exercise; it is the same translation skill needed to write a working formula or program.
Types of Expressions
| Type | Example |
|---|---|
| Numerical expression | 3 + 7 × 2 − 4 |
| Algebraic expression | 3x + 7 − 2y |
| Complex expression | (x² + 2x) ÷ (x + 1) |
Parts of an Expression
- Terms: the parts separated by + or − signs. In 3x + 7 − 2y there are three terms.
- Coefficient: the number in front of a variable. In 3x, the coefficient is 3.
- Constant: a term with no variable. In 3x + 7, the constant is 7.
Writing Expressions from Words
| Words | Expression |
|---|---|
| Seven more than twice a number n | 2n + 7 |
| Three less than a quarter of x | x/4 − 3 |
| The product of 5 and the sum of a and b | 5(a + b) |
Simplifying Expressions
4x + 3 − 2x + 8 = (4x − 2x) + (3 + 8) = 2x + 11
Key Takeaways
- An expression has no equals sign; an equation does.
- Expressions can be simplified by collecting like terms.
- Recognise parts: terms, coefficients, constants, and variables.
Practice: Arithmetic Expressions
Find the Coefficient