Order of math operations - what are the rules?

The order in which the actions are performed helps in the correct counting. Check the order before you start doing the math problems.

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1. The order of arithmetic operations

Arithmetic is the part of mathematics that deals with working with numbers. It has certain rules thanks to which we are able to properly perform mathematical operations. The basic rules apply to the sequence of actions and are as follows:

  1. First, we perform actions in parentheses (according to the order in which actions are performed).
  2. Once we figure out what's in the parentheses, we move on to exponentiation and square root.
  3. Then we do multiplication or division.
  4. At the very end, we perform addition or subtraction.

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2. The order of performing mathematical operations

Now let's see the math operation below and figure out how to calculate it correctly.

Example: 10 + 5 x 2 =?

If we did the calculation and apply the rule from left to right, without taking into account any other rules, we would get a result of 30. This would be the result of two steps - the first step would be adding 10 + 5 which is 15, the second would be multiplying 15 x 2 which is 30.

However, taking into account the rules that apply to the sequence of actions, a completely different result comes out. First, we do the multiplication, which is 5 x 2, which gives the value 10.

Only now can we take the second step, which is adding; we add 10 + 10, which gives the correct result 20.

By applying the rules of the sequence of actions, we get a different result than by performing actions from left to right.

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3. The sequence of actions - addition and subtraction

For operations where only addition and subtraction occur, we count everything from left to right. For example:

20 − 5 + 10 = 15 + 10 = 25

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4. Sequence of operations - multiplication and division

The situation is similar in the case of multiplication and division. If we only work with multiplication and division, then we also count everything using the rule from left to right.

For example:

30: 5 x 2 = 6 x 2 = 12

5. Sequence of actions - powers

Another important principle is about the powers in action. If there are powers in a mathematical operation, they are given priority, which means that they should be the starting point for solving a problem.

Here are some examples of activities:

48 : 2² = 48 : 4 =12 50 : 5² = 50 : 25 = 2

And what happens when different activities emerge? Then we also start by calculating the power, next is multiplication and division (from left to right), and finally addition and subtraction (also from left to right).

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6. The order of operations in parentheses

When an activity contains parentheses, we start by computing what is in the parentheses and then we move on to the sequence rules for actions. For example:

8 x (2 + 2) = 8 x 4 = 32

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