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.
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 Questions
- Identify all terms in: 5x² − 3x + 7.
- Write the expression: "four more than three times y".
- Simplify: 6a − 2b + 3a + 5b.
- What is the coefficient of x in 7x − 4?
- Simplify: 2(3x + 4) − 5x.