Use Brackets in Calculations to Give Different Answers

In this activity, we will learn how putting brackets in different places gives different answers.

Remember that with a string of operations, they must be done in the following order:

Brackets
Powers or indices
Division

Multiplication
Adding and subtracting

Remember BIDMAS  or BODMAS

Example
 

3 +  5 × 6 - 2 × 3 + 4

There are no brackets, powers or division, so the first thing to do is multiplication.

5 x 6 = 30 and 2 x 3 = 6

We can now insert those two answers back into the original calculation:

3 + 30 - 6 + 4

Now we add and subtract:

3 + 30 = 33 and -6 + 4 = -2

33 - 2 = 31

If we put brackets in different places, we will get a different answer.

(3 + 5) × 6 - 2 × (3 + 4)

Do the brackets first: 3 + 5 = 8 and 3 + 4 = 7

Insert those two answers back into the original calculation:

8 x 6 - 2 x 7

Then multiply:

8 x 6 = 48 and 2 x 7 = 14

Insert them back into the calculation:

48 - 14 and finally subtract:

48 - 14 = 34
 

So, can you see that exactly the same numbers and signs can give you a completely different answer if brackets are added to the calculation?