How to solve mathematical equations in parentheses
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Algorithm No. 1

To solve simple problems without parentheses, and calculate roots and fractions, remember the following rules:

  • We perform all actions from left to right.
  • First multiply and divide, then add and subtract.

How to use these rules?

Example No. 1. Calculate: 15 – 3 + 7.

First, perform all actions from left to right:

  1. 15 – 3 = 12
  2. 12 + 7 = 19

Answer: 15 – 3 + 7 = 19.

Example No. 2. Calculate: 10 ÷ 2 x 8.

Here we also perform operations from left to right:

  1. 10 ÷ 2 = 5
  2. 5 x 8 = 40

Answer: 10 ÷ 2 x 8 = 40.

Example No. 3. Calculate: 5 x 4 – 8 ÷ 2.

Also perform calculations from left to right, but remember that multiplication and division occur first. So:

  1. 5 x 4 = 20. This is the multiplication that occurs first when viewed from left to right.
  2. 8 ÷ 2 = 4. This is division, and although it follows subtraction, it has priority.
  3. 20 – 4 = 16. Now the usual order: after multiplication and division, we move on to subtraction.

Answer: 5 x 4 – 8 ÷ 2 = 16.

If you have multiple actions to perform, you can number them so you remember the correct order.The bright side

If you have multiple actions to perform, you can number them so you remember the correct order.

Important: There is no need for parentheses if addition and subtraction are done from left to right. For example, instead of (4 – 2) + 3, you could simply write 4 – 2 + 3. There's also no need for parentheses when prioritizing actions anyway. For example, instead of 5 + (4 x 3), you could just write 5 + 4 x 3 because multiplication takes precedence anyway.

Algorithm No. 2The bright side

Algorithm No. 2

A mathematical expression can contain parentheses that change the usual order in which operations are performed. To make correct calculations, remember the following rules:

  • All operations in parentheses are performed first.
  • Then perform the remaining actions from left to right.
  • Multiplication and division are always done first, followed by subtraction and addition.
  • The same rules apply to brackets.
  • If fractures or fractures are present, they should be evaluated (if possible) before all other operations.

Example No. 1. Calculate: 5 x (8 – 4) ÷ 2.

Do the operations in parentheses first, then follow the usual order:

  1. 8 – 4 = 4. Knowing the result in parentheses, we can write 5 x (8 – 4) ÷ 2 = 5 x 4 ÷ 2. Then follow the order:
  2. 5 x 4 = 20
  3. 20 ÷ 2 = 10

So 5 x (8 – 4) ÷ 2 = 10.

Answer: 5 x (8 – 4) ÷ 2 = 10.

Example No. 2. Calculate and compare the results: 7 – 3 + 2 and 7 – (3 + 2).

Calculate the result of the first expression: 7 – 3 + 2 = 6. Now calculate the result of the second expression: 7 – (3 + 2) = 7 – 5 = 2. The parentheses in the second example have changed their order of operations, so the results are different.

Example No. 3The bright side

Example No. 3

Example No. 3. Calculate 8 – 2 x (15 – 4 x 3) + (7 + 3 x 2).

At first glance, this expression seems complicated. To simplify the process, break it down into separate activities:

  1. Do the operations in parentheses first. To get the right result on the first slide, it's important to remember which activities are a priority. So first calculate 4 x 3 and then subtract the result from 15. The answer is 3. Do the same with the second bracket – calculate 3 x 2 and add 7. The result is 13.
  2. Now write 8 – 2 15.

Important: You may sometimes encounter expressions in which parentheses are inside other parentheses. The principle is the same: first calculate everything between the inner parentheses, then the outer ones, and then do the rest of the calculations. Different parentheses are used – in most cases this is (), but you can also use { } and [ ].

The multiplication symbol before the parentheses has been removed, which may cause errorsThe bright side

The multiplication symbol before the parentheses has been removed, which may cause errors

  • The multiplication symbol before the parentheses has been removed, which may cause errors.

For example, we have the following expression: 8 + 4(3 – 1). When solving this task, it is easy to get confused in the order. The correct order is as follows: First calculate the result in parentheses, then multiply it by 4 and add the result to 8. Thus we get: 8 + 4(3 – 1) = 8 + 4 x (3 – 1) = 8 + 4 x 2 = 8 + 8 = 16.

In this case, things get more complicated: 8 ÷ 4(3 – 1). But the order is the same. First the parentheses, then division and multiplication from left to right: 8 ÷ 4 x (3 – 1) = 8 ÷ 4 x 2 = 2 x 2 = 4.

Incorrect removal of parentheses preceded by a minus signThe bright side

Incorrect removal of parentheses preceded by a minus sign

  • Incorrect removal of parentheses preceded by a minus sign
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