Calculate the numerical value of an expression

Replacing a letter with a number

Calculating the numerical value of a literal expression involves replacing each letter with a given number, then carrying out the calculation whilst observing the order of operations (brackets, then multiplication, then addition/subtraction).

Example: for E = 2x + 3, let’s calculate E when x = 5. E = 2 × 5 + 3 = 10 + 3 = 13

An example with several values

x	Expression 3x - 4	Result
0	3 × 0 − 4	−4
2	3 × 2 − 4	2
5	3 × 5 − 4	11

We can see that the value of the expression changes depending on the value given to x: this is to be expected, as x is a variable.

Be careful with negative numbers

When x is negative, we often put the value in brackets to avoid sign errors.

Example: F = x² - 4, for x = -3 F = (-3)² - 4 = 9 - 4 = 5

Note: (-3)² = 9 (positive), but -3² (without brackets) would be interpreted as -(3²) = -9. The brackets are essential!

Common pitfall

Failing to follow the order of operations is the most common mistake. In G = 5 + 2x, for x = 4, you must first calculate 2x4 = 8, then add 5: G = 13. Many pupils mistakenly calculate 5 + 2 first, then x × 4, which gives an incorrect result (28 instead of 13).