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Priority of Operations

Priority of Operations

Adding, Subtracting, Multiplying and Dividing are called operators. Operators perform actions on numbers.  

There are other operators, such as indices - these control operations such as squaring a number, or finding a square root.

Brackets ( ) are used to control the order in which calculations take place.

Each operation has a priority and control the sequence in which calculations are carried out:

• Brackets are always calculated first;

• Indices - such as 32 - are calculated next;

• Divide - is next;

• Multipy (actually has the same priority as Division);

• Add - is then next;

• Subtract - (same priority as Addition).

This is known as BIDMAS (taking the first letter of each operation); sometimes it is also known as BODMAS.

When there is a mixture of operations in a calculation, the sequence of operations must be carried out in BIDMAS order.

Example 1

Ellie has calculated 4 + 6 ÷ 2 = 5.  Is she correct?

BIDMAS rules. The division has a higher priority than the addition and must be carried out first: 6 ÷ 2 = 3.

Then carry out the addition 4 + 3 = 7. 

Answer: No

Example 2

Put in brackets to make this calculation correct: 3 + 42 = 49

Put brackets before the 3, and between the 4 and 2

The brackets make sure the addition is carried out first.

Answer: (3 + 4)2 = 49

See also Squares and Calculating with Indices