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Parentheses Definition Geometry

Introduction to Parentheses

Parentheses, also known as round brackets, are symbols used in pairs to group things together. The parentheses symbol is represented as ( ). The parentheses in Math are used to group numbers, variables, or both together.

Example:

4 ( 5 - 4) = 4 1 = 4

In the above example, the parentheses group (5 - 4), tell us to calculate the bracket first.


What are parentheses in math?

Parenthese are symbols ( ) used in pairs to group things together. In general, it is important or convenient to manually choose which order of operation should occur first in Math. Generally, we evaluate exponents first, then multiplication and division in second, then finally addition and subtraction at last. We choose this order of operation, unless the given Mathematical expression is surrounded by the parenthesis.


Generally, we evaluate, 5 3 + 62 like this 5 3 + 36 = 15 + 36 = 51. However, if parentheses are added, we need to calculate the terms inside the bracket or parenthesis first.


For example,

Starting with the innermost set of parentheses and calculating, we have:

(5 (3 + 6) )2 = (5 (9))2 = (5 9)2 = (45)2 = 2025.


Parentheses Definition in Math

Parenthesis, also known as round brackets, are defined as the symbols in Math. Parenthesis are primarily used in Mathematics/Algebraic equations to modify the normal order of operation. Hence, in Mathematic expressions involving Parentheses, the terms inside the bracket or parenthesis are calculated first.


For example, In an expression like (2 + 5) 6, the part of Mathematical expression within the parenthesis is calculated first ( 2 + 5) = 7, then this result is used to calculate the rest of the expression 7 6 = 42. Therefore, (2 + 5) 6 = 42.


Parentheses Example:

What is ( (2 + 3)2 + 4 ) 7 ?

Solution:

Following the precise order of operation, we get the following:

( (2 + 3)2 + 4 ) 7 Adding terms inside the small parentheses gives

= ( (5)2 + 4 ) 7 Calculating the exponents inside the small parentheses gives

= ( 25 + 4) 7 Adding the terms inside the parentheses.

= (29) 7 Multiplying the terms gives

= 203 Result


Parentheses Rules

The four important parentheses rules are discussed below:

  • x + (- y) =  x - y

Example: 5 + (-3) = 5 - 3 = 2

  • x - (- y) = x + y

Example: 5 - (- 3) = 5 + 3 = 8

  • x . (-y) = - xy 

Example: 5 . (-3) = - 15

  • (-x) (-y) = xy

Example: (-5) (-3) = 5 3 = 15


Parentheses Example With Solution

1. Simplify the expression (2 + 5 7) - (3 + 4)

Solution:

Here, the expression has two parentheses. We will solve the terms inside both the parentheses separately and then combine the result to get the answer.

Let’s first solve, (2 + 5 7)

Here, according to the order of operation, we will multiply 5 and 7 first. Accordingly,

(2 + 35) = 2 + 35 = 37

Now, we will solve (3 + 4), which gives 7.

Combining, both the results, we get

(2 + 5 7) - ( 3 + 4) = 37 - 7 = 30

Therefore, ( 2 + 5 7) - ( 3 + 4) = 30


Example 2:

Solve (3 + 52)2

Solution:

The parentheses tell us we must evaluate the expression first 3 + 52 and then square it. Here, ensure to evaluate 5² first before adding. This is because according to the order of operation, we first evaluate exponents. Accordingly,

(3 + 52)2 = (3 + 25)2 = (28)2 = 784.

Therefore, (3 + 52)2 is equal to 784.


Do You Know?

In Math, the order of operation are the rules that describe the sequence in which the multiple arithmetic operations in an expression are solved. The best way to remember the order of operations is PEMDAS.


As per the PEMDAS rule, solve

  • P = Parentheses first

  • E = Exponents ( Power and Square Roots, etc)

  • MD = Multiplication and Division (Left to Right or whichever comes first)

  • AS = Addition and Subtraction (Left to Right or whichever comes first)


Conclusion:

In short, parentheses or round brackets are renown mathematical symbols used in parts to group things together or to specify the order of operation in an equation. In Math, parentheses are used in two different ways i.e. to multiply and to tell what numbers to look at first.

FAQs on Parentheses Definition Geometry

1. What are the three main uses of parenthesis in Mathematics?

The three main uses of parentheses in Mathematics are:

  • To separate numbers for clarity.

  • To represent multiplication and,

  • To group numbers together.

2. Does parentheses mean multiplication?

Yes, parentheses does not only mean order of operations but it also represents multiplication. For example, 4(5) is equivalent to 4  × 5 = 20.

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