We will learn the uses of brackets, we have learnt about the precedence of fundamental operations of addition, subtraction, multiplication and division. According to it, the order in which operations are to be performed is first division, then multiplication after which addition and finally subtraction. But sometimes in some complex expressions, we require a set of operations to be performed prior to the others.

For example, if we want an addition to be performed before a division or a multiplication, then we need to use brackets. A bracket indicates that the operations within it are to be performed before the operations outside it.

For example, the expression 12 ÷ 3 x 4, as per **DMAS rule** where ‘D’ stands for division, ‘M’ for multiplication, ‘A’ for addition and, ‘S’ for subtraction, *is simplified by first dividing 12 by 3 and then multiplying by 4 as shown below: *

12 ÷ 3 x 4 = (12 ÷ 3 ) x 4 = 4 x 4 = 16.

However, if we wish to multiply 3 and 4 first and then divide 12 by the resulting number, we write the expression as 12 ÷ (3 x 4) and simplify it as;

12 ÷ (3 x 4) = 12 ÷ 12 = 1.

In **complex expressions**, sometimes, it is necessary to have brackets within brackets. Since same type of brackets one within another can be confusing, so different types of brackets are used. Most commonly used brackets are shown below with symbol and names to identify.

**Brackets symbol Name ** ** ( )** Parentheses or common brackets ** { } ** Braces or Curly brackets ** [ ] ** Brackets or square brackets or box brackets ** _ ** Vinculum

The left part of each bracket symbol indicates the start of the bracket and the right part indicates the end of the bracket.

In writing mathematical expressions consisting of more than one bracket, parenthesis is used in the innermost part followed by braces and these two are covered by square brackets. Uses of brackets are required for a set of operations to be performed prior to the others.

● Numbers - Integers

**Properties of Multiplication of Integers**

**Examples on Multiplication of Integers**

**Properties of Division of Integers**

**Examples on Division of Integers**

**Examples on Fundamental Operations**

● Numbers - Worksheets

**Worksheet on Multiplication of Integers**

**Worksheet on Division of Integers**

**Worksheet on Fundamental Operation**

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