**Brackets | What are
brackets?**

**Brackets** are the symbols used to enclose certain variable or numerical expressions that are to be
taken together. Brackets are used to change the order in which the operations
are to be done.

For example, 7×2+3 = 14+3=17. But, if the sum has to be done at
first, then we put brackets within 2+3, i.e. 7×(2+3) = 7×5 = 35.

**Types of brackets**

There are 3 types of brackets. They are:

( ) Parenthesis or small
brackets

{ } Middle brackets or
curly brackets

[ ] Big brackets or square
brackets

**Order of use of the brackets**

When all three types of brackets are in an expression, then we
first have to solve within the small brackets( ), then curly brackets{ } and at
last the square brackets[ ].

**BODMAS Rule**

In simplification of integers under the relation of basic
operations addition(+), Subtraction(-), multiplication, division(÷) along with
the use of brackets, we have to follow the **BODMAS
Rule**.

**BODMAS Full Form**

The full form of **BODMAS**
is, **B** for Brackets, **O** for Of, **D** for Division, **M** for
Multiplication, **A** for Addition and **S** for Subtraction.

**Meaning of BODMAS
Rule**

According to **BODMAS**
rule, first we have to follow the Brackets, second Of, third Division, fourth Multiplication,
fifth Addition, and sixth Subtraction.

There may be sometimes a Vinculum inside the brackets. Vinculum
is an overline for certain numbers. And, we have to solve the numbers under the
vinculum at first.

Here is the table for order of operation according to the BODMAS rule.

Here are some BODMAS Questions with Answers:

**Worked Out Examples**

**Example 1:** Simplify: 7 + 8 – 9 ÷ 3 × 2

**Solution:** Here,

7 + 8 – 9 ÷ 3 × 2

= 7 + 8 – 3 × 2

= 7 + 8 – 6

= 15 – 6

= 9 Ans.

**Example 2:** Simplify: 54 ÷ [{16 – (3 – 2)} – 6]

**Solution:** Here,

54 ÷ [{16 – (3 – 2)} – 6]

= 54 ÷ [{16 – 1} – 6]

= 54 ÷ [15 – 6]

= 54 ÷ 9

= 6 Ans.

**Example 3:** Simplify: 52 – 4 of (17 – 12) + 4 × 7

**Solution:** Here,

52 – 4 of (17 – 12) + 4 ×
7

= 52 – 4 of 5 + 4 × 7

= 52 – 20 + 4 × 7

= 52 – 20 + 28

= 80 – 20

= 60 Ans.

**Example 4:** Simplify:

**Solution:** Here,

**Example 5:** Simplify:

**Solution:** Here,

**Example 6:** Simplify: 13 × 5 ÷ [{12 ÷ (4 – 2)} – 2]

**Solution:** Here,

13 × 5 ÷ [{12 ÷ (4 – 2)} –
1]

= 13 × 5 ÷ [{12 ÷ 2} – 1]

= 13 × 5 ÷ [6 – 1]

= 13 × 5 ÷ 5

= 13 × 1

= 13 Ans.

**Example 7:** Simplify: 8 × 3 + [63 ÷ {18 ÷ 3 (9 – 17 + 5 × 2)}]

**Solution:** Here,

8 × 3 + [63 ÷ {18 ÷ 3 (9 –
17 + 5 × 2)}]

= 8 × 3 + [63 ÷ {18 ÷ 3 (9
– 17 + 10)}]

= 8 × 3 + [63 ÷ {18 ÷ 3 of
2}]

= 8 × 3 + [63 ÷ {18 ÷ 6}]

= 8 × 3 + [63 ÷ 3]

= 8 × 3 + 21

= 24 + 21

= 45 Ans.

**BODMAS in Fractions:**

**Example 8:** Simplify:

**Solution:** Here,

**
**

**Example 9:** Simplify:

**Solution:** Here,

**Example 10:** Simplify:

**Solution:**Here,

If you have any questions or problems regarding the **Brackets and BODMAS Rule**, you can ask here, in the comment section below.

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