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Home > Maths I > Relationships > Formulae

Maths I



Mathematics is full of rules. In mathematics, another word for a rule is a formula. This section deals with constructing a formula, and using it to work out values. We shall also look at forming algebraic equations.

Evaluating a formula

Remember BODMAS? It means we have to work out first, the bit inside brackets, if there are any. Division and multiplication are done before addition and subtraction.

  • B: Calculate anything inside brackets first.
  • O: Next, work out the others (i.e. powers and square roots, etc.).
  • DM: In the next step, do any division and multiplication (working from left to right)
  • AS: Finally, do any addition and subtraction (working from left to right).

Example 1

A cashier used the formula below, to work out plumbers' wages.

W = 7(N + 1.5E + 2S)


  • \pounds{W} is the weekly wage.
  • N is the number of hours in a normal working week.
  • E is the hours worked in the evening.
  • S is the hours worked on a Saturday.

Example 2

Calculate the wages of a plumber whose normal working week is 40 hours, and who worked 4 hours in the evening, and 6 hours on Saturday.

A plumber grinning with his plunger.

We are told N = 40, E = 4 and S = 6.

Put these values into the formula:

W = 7(40 + 1.5 \times 4 + 2 \times 6)

= 7(40 + 6 + 12) Work inside the brackets first. Multiplication before addition

= 7 \times 58

= 406

Therefore the wages are \pounds406.

Now try this question.


Use the formula \;W = 7(N + 1.5E + 2S) to find the weekly wage of a plumber whose normal week is \;35 hours and who worked \;6 hours in the evening and \;3\; hours on Saturday.


N = 35, E = 6, S = 3

W = 7(35 + 1.5 \times 6 + 2 \times 3)

= 7(35 + 9 + 6)

= 7 \times 50

= 350

The wages are \pounds{350}


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