What is a numerical expression?
A numerical expression is a maths phrase made of numbers and operations, such as:
- 5 + 8
- 3 × (12 − 4)
- 2³ + 6 ÷ 2
It has no equals sign. When you evaluate an expression, you find its single value.
Expression vs equation
| Expression | Equation |
|---|---|
| 4 × 7 + 2 | 4 × 7 + 2 = 30 |
| A phrase | A sentence |
| Has a value | States two values are equal |
| You evaluate it | It can be true or false |
Terms
Parts of an expression separated by + or − are called terms.
- 6 + 4 × 3 − 8 has three terms: 6, 4 × 3, and 8.
Thinking in terms helps: work out each term, then add or subtract them.
Evaluating
Use the order of operations (BEDMAS).
Example: 3 × (12 − 4) − 2²
- Brackets: 8 → 3 × 8 − 2²
- Exponents: 4 → 3 × 8 − 4
- Multiply: 24 − 4
- Subtract: 20
Writing expressions from words
| Words | Expression |
|---|---|
| 7 more than 15 | 15 + 7 |
| 9 less than 20 | 20 − 9 |
| twice the sum of 3 and 5 | 2 × (3 + 5) |
| the quotient of 36 and 4 | 36 ÷ 4 |
| 3 times 8, minus 5 | 3 × 8 − 5 |
| half of 18, then add 6 | 18 ÷ 2 + 6 |
Watch out: "9 less than 20" is 20 − 9, not 9 − 20.
Interpreting expressions without calculating
You can compare expressions using reasoning:
- 3 × (452 + 89) is three times as large as 452 + 89.
- 456 × 8 is greater than 456 × 7 (one more group of 456).
Using brackets to change meaning
| Expression | Value |
|---|---|
| 2 + 3 × 4 | 14 |
| (2 + 3) × 4 | 20 |
| 20 − 8 − 2 | 10 |
| 20 − (8 − 2) | 14 |
Worked examples
Example 1: Evaluate 18 ÷ 3 + 4 × 2.
6 + 8 = 14.
Example 2: Write an expression for "subtract 4 from 10, then multiply by 6", and evaluate.
(10 − 4) × 6 = 36.
Example 3: Without calculating, which is larger: 5 × (37 + 63) or 5 × 37 + 63?
The first multiplies all of 100 by 5 (500); the second only multiplies 37 (248). The first.
Common mistakes
- Writing subtraction backwards from "less than" phrases.
- Forgetting brackets for "the sum of … times".
- Putting an equals sign in the middle of a calculation chain like 4 + 5 = 9 × 2 = 18 (9 × 2 isn’t equal to 4 + 5).
Try it yourself
- Evaluate 4 + 6 × 2 − 1.
- Evaluate (4 + 6) × (2 − 1).
- Write: "8 less than the product of 7 and 6".
- How many terms are in 5 × 2 + 9 − 3 × 4?
- Is 3 + 4 = 7 an expression or an equation?
Answers: 1) 15 2) 10 3) 7 × 6 − 8 = 34 4) three 5) an equation
Quick recap
- A numerical expression combines numbers and operations without an equals sign.
- Evaluate using the order of operations.
- Translate words carefully and use brackets where needed.