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1.1 J) BODMAS/ BIDMAS – Part 2
The content in this section builds on the content that was discussed in the previous section. Make sure that you have covered the content in the previous section before working through the content in this section (click here to be taken through to the previous section).
 
A reminder of what BODMAS stands for is given below:
  • Brackets
  • Other
  • Division
  • Multiplication
  • Addition
  • Subtraction

The letters in BIDMAS mean the same as the letters in BODMAS, except the I in BIDMAS means indices and not other. ​

Example 1 – Involving Brackets

Whenever we are working with brackets, we always calculate the value inside the brackets by using BODMAS. If there is a bracket inside another bracket, we calculate the bracket that is inside the other bracket first (see example 2).

 

Complete the calculation below:

Picture

The first step of BODMAS is the B, which stands for brackets. Therefore, we need to calculate what the value is in the first bracket; we need to calculate what 4 + 2 is. We would need to follow the rules of BODMAS for this bracket, but as there is only one operation, we just add 4 and 2 together. The calculation becomes:

Picture

As we have dealt with the bracket, we are now able to work through the other components in BODMAS starting with other/ indices; the 62.

Picture

We now move on to the division; 60 ÷ 5. The calculation becomes:

Picture

We are now onto the M in BODMAS, which is multiplication. There is no multiplication taking place in this calculation, thus meaning that we move on to addition. There is no addition, so we move onto subtraction; 36 – 12.

Picture

Therefore, the answer to the calculation is 24.


Example 2

Complete the calculation below:

Picture

There are 3 sets of brackets in the calculation above. There are two sets of brackets on the left and one of the brackets is inside the other bracket. We calculate the bracket that is inside the other bracket first. Therefore, we are going to calculate (3 x 4 – 3) first. We calculate it according to BODMAS. Multiplication comes before subtraction, so we multiply 3 by 4 first. This bracket becomes:

Picture

We now move onto the subtraction; 12 – 3, which is 9.

Picture

We can sub this into the original calculation.  

Picture

We now have two separate brackets with no brackets inside either of them. Therefore, we calculate each of the brackets according to BODMAS. Let’s do this for the first bracket first; (42 – 9). We start with the other/ indices; 42.

Picture

We are now able to complete the subtraction; 16 – 9.

Picture

We now do the same with the second bracket; (72 x 22). We need to complete the other/ indices first; the 72 and 22. This bracket becomes:

Picture

We now complete the multiplication; 49 x 4.

Picture

Therefore, the second bracket is 196.

 

We now place the outcome for the first and second bracket back into the calculation; the first bracket is 7 and the second bracket is 196.

Picture

We now complete the addition.

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Therefore, the answer to this calculation is 203.


Final Notes

You will sometimes need to be careful when you are working out calculations like this on a calculator as some calculators will not follow the rules of BOAMAS. Therefore, it is sometimes easier and more accurate to complete these calculations on paper rather than using a calculator.

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