Functional Skills: BIDMAS

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Functional Skills: BIDMAS Revision

BIDMAS

BIDMAS (sometimes known as BODMAS) helps us remember the order in which we perform mathematical operations. The letters stand for:

  • Brackets
  • Indices (or Orders)
  • Division
  • Multiplication
  • Addition
  • Subtraction

Make sure you are happy with the following topics before continuing.

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Notes:

  • For division and multiplication, work them out in the order that they appear (from left to right) in the question.
  • For addition and subtraction, when they are the only two operations left in the sum, work them out in the order that they appear (from left to right).

BIDMAS Calculations

Example: Calculate 5 \times(2^2 + 4) - 7

Step 1: The first letter of BIDMAS is B, so look inside the brackets first. (If there are no brackets, look at indices, and then division etc.)

In the brackets there are two operations: an index/power and an addition. The letter I comes before the letter A in BIDMAS so first work out the result of 2^2 and then add it to 4.

(2^2 + 4) = (4 + 4) = 8

Step 2: There is a multiplication and a subtraction left, so because M comes before S, do the multiplication first and then the subtraction,

5 \times 8 - 7 = 40 - 7 = 33

So,

5 \times(2^2 + 4) - 7 = 33

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BIDMAS with Fractions

For BIDMAS with fractions, work out the values of the top and bottom of the fraction separately, and then simplify the fraction if possible.

Example: Calculate \dfrac{4 \times 3 - 5}{11 + (15 \div 5)} and simplify your answer.

Step 1: Firstly, look at the top of the fraction. There is a multiplication and a subtraction, so we do the multiplication first and the subtraction second.

4 \times 3 - 5 = 12 - 5 = 7

Step 2: Now, look at the bottom. This contains a division inside the brackets, so do this calculation first, and then perform the addition.

11 + (15 \div 5) = 11 + 3 = 14

Step 3: Therefore, the fraction is \dfrac{7}{14}

The top and bottom of the fraction can both be divided by 7, so the answer can be simplified to

\dfrac{7}{14} = \dfrac{1}{2}

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Functional Skills: BIDMAS Example Questions

Firstly, perform the operations inside the brackets (B),

 

12 \div 3 = 4

 

Then move onto the indices (I),

 

(4)^2 = 16

 

Finally, do the multiplication (M),

 

15\times 16= 240

There are 2 brackets (B) to calculate first,

(2 \times 3^3) and (17-11)

 

Inside the first bracket, there is an index (I),

 

2 \times 3^3 = 2 \times 27

 

Calculate any divisions (D) or multiplications (M), followed by additions (A) or subtractions (S) inside the brackets,

 

(2 \times 27 = 54)     and     (17-11 = 6)

 

Finally, complete the calculation,

 

\begin{aligned} 54 \div 6 &= 9 \\ (2 \times 3^3) \div (17 - 11) &= 9 \end{aligned}

Firstly, look at the top of the fraction.

There are no brackets, but there is an index (I),

3^2 = 9

Next, do the multiplication (M),

2 \times 3 = 6

Then, do the subtraction (S),

9 - 6 = 3

 

Now, look at the bottom of the fraction,

There is only a division (D), so do that,

24 \div 2 = 12

 

So, the fraction is \dfrac{3}{12} which can be simplified to \dfrac{1}{4}

Additional Resources

PFS

Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: BIDMAS Worksheet and Example Questions

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