### Order of operations

Sometimes you will see a calculation written in the form  $${\text{8 - (2 x 3)}}$$ , where brackets, that is the symbols $$($$ and $$)$$, are put around part of the calculation.
Brackets are  there to tell you to carry out the calculation inside them first. So  $${\text{8 - (2x3 ) = 8 - 6 = 2}}$$.
If you had to find the answer to $${\text{8 }} + {\text{ 5 }} - {\text{ 3}}$$ , you might wonder whether to do the addition first or  the subtraction first.
If you do the addition first,  $${\text{8 }} + {\text{ 5}} - {\text{ 3 }} = {\text{ 13}} - {\text{ 3 }} = {\text{ 1}}0$$.

If you do the subtraction first,  $${\text{8 }} + {\text{ 5}} - {\text{ 3 }} = {\text{ 8 }} + {\text{ 2 }} = {\text{ 1}}0$$ .

In this case, it makes no any difference which operation you do first.

If, however, you had to find the answer to  $${\text{3 }} + {\text{ 4x2}}$$ , your answer will depend on whether you do the  addition first or the multiplication first.
If you do the addition first,  $${\text{3 }} + {\text{ 4x 2 }} = {\text{ 7x 2 }} = {\text{ 14}}$$.

If you do the multiplication first,  $${\text{3 }} + {\text{ 4x 2 }} = {\text{ 3 }} + {\text{ 8 }} = {\text{ 11}}$$.

To avoid confusion, mathematicians have decided that, if there are no brackets, multiplication and  division are carried out before addition and subtraction.

Such a rule is called a convention: clearly the opposite decision  could be  made,  but  it  has  been  agreed  that the  calculation $${\text{3 }} + {\text{ 4x 2}}$$  should be carried out as  $${\text{3 }} + {\text{ 4x 2 }} = {\text{ 3 }} + {\text{ 8 }} = {\text{ 11}}$$.

There are  a  number of these conventions, often  remembered by  the word 'BoDMAS', which stands for:

• Brackets
• Divide
• Multiply
• Subtract

This  is  the order  in  which arithmetic operations must be carried out.
Most  calculators  have  the  'BoDMAS '  convention  programmed into them, and so automatically carry out operations in the correct order.

5195 x

Evaluate each expression.

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3078 x

Evaluate each expression.

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2844 x

Evaluate each using the values given.

This free worksheet contains 10 assignments each with 24 questions with answers.

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