OPERATIONS WITH GROUPING SIGNS (WITH EXERCISES) - MATHS - 2025

The operations grouping symbols indicate the order to be performed a mathematical operation as an addition, subtraction, or division product. These are widely used in elementary school. The most commonly used mathematical grouping signs are parentheses "()", square brackets "", and braces "{}".

When a mathematical operation is written without grouping signs, the order in which it should be done is ambiguous. For example, the expression 3 × 5 + 2 is different from the operation 3x (5 + 2).

Although the hierarchy of mathematical operations indicates that the product must be solved first, it really depends on how the author of the expression thought it.

How do you solve an operation with grouping signs?

In view of the ambiguities that can occur, it is very useful to write the mathematical operations with the grouping signs described above.

Depending on the author, the aforementioned grouping signs may also have a certain hierarchy.

The important thing to know is that you always start by solving the most internal grouping signs, and then move on to the next ones until the entire operation is carried out.

Another important detail is that everything within two equal grouping signs must always be resolved before moving on to the next step.

Example

The expression 5+ {(3 × 4) +} is solved as follows:

= 5+ {(12) +}

= 5+ {12 + 6}

= 5+ 18

= 23.

Exercises

Below is a list of exercises with mathematical operations where the grouping signs must be used.

First exercise

Solve the expression 20 - {+ (15/3) - 6}.

Solution

Following the steps outlined above, you should start by first solving each operation that falls between two equal grouping signs from the inside out. Thus, 20 - {+ (15/3) - 6}

= 20 - {+ (5) - 6}

= 20 - {+ 5 - 6}

= 20 - {3 - 1}

= 20 - 2

= 18.

Second exercise

Which of the following expressions results in 3?

(a) 10 - {x2 - (9/3)}.

(b) 10 -.

(c) 10 - {(3 × 2) + 2x}.

Solution

Each expression must be observed very carefully, then solving each operation that is between a pair of internal grouping signs and moving forward.

Option (a) returns -11, option (c) returns 6, and option (b) returns 3. Therefore, the correct answer is option (b).

As can be seen in this example, the mathematical operations carried out are the same in the three expressions and are in the same order, the only thing that changes is the order of the grouping signs and therefore the order in which they are carried out. said operations.

This change of order affects the entire operation, to the point that the final result is different from the correct one.

Third exercise

The result of the operation 5x ((2 + 3) x3 + (12/6 -1)) is:

(a) 21

(b) 36

(c) 80

Solution

Only parentheses appear in this expression, therefore care must be taken to identify which pairs must be solved first.

The operation is solved as follows:

5x ((2 + 3) x3 + (12/6 -1))

= 5x ((5) x3 + (2 -1))

= 5x (15 + 1)

= 5 × 16

= 80.

Thus, the correct answer is option (c).

References

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