The order of arithmetic operations (operations)

And in the calculations of examples you need to follow a certain procedure. Using the rules below, we will figure out in which order actions are performed and why brackets are needed.

If there are no brackets in the expression, then:

• first we perform all the multiplication and division actions from left to right;
• and then from left to right all the actions of addition and subtraction.

Consider the procedure in the following example.

We remind you that the order of actions in mathematics is placed from left to right (from the beginning to the end of the example).

When calculating the value of an expression, you can record in two ways.

First way

• Each action is recorded separately with its number under the example.
• After the last action is completed, the answer is necessarily recorded in the original example.

When calculating the results of actions with two-digit and / or three-digit numbers, be sure to bring your calculations in a column.

Second way

• The second method is called "chain" writing. All calculations are performed in exactly the same procedure, but the results are recorded immediately after the equal sign.

Inside the brackets themselves, there is a rule of procedure as in expressions without brackets.

If there are another brackets inside the brackets, then the actions inside nested (internal) brackets are performed first.

Procedure and exponentiation

If the example contains a numeric or alphabetic expression in brackets that must be raised to a power, then:

• First we perform all the actions inside the brackets.
• Then we raise to the power all the brackets and numbers standing in the power, from left to right (from the beginning to the end of the example).
• Perform the remaining actions in the usual manner.