BODMAS Rule (Mathematics)- Simplification BODMAS rule, rule, methods, solution with the help of various examples and short methods to solve simplification questions in exam

## Rule for Simplification BODMAS rule, tricks, methods, solution with the help of various examples and short methods to solve simplification questions in exam

**Name of Rule**: **BODMAS Rule**

B: Bracket

O: of

D: Division

M: Multiplication

A: Addition

S: Subtraction

Thus, simplifying an expression, first of all brackets must be removed, strictly in the Order:

- ()
- {}
- []

After removing the bracket, we must use the following operations strictly in order

- Of
- Division
- Multiplication
- Addition
- Subtraction

**Question 1) 5005 – 5000 ÷ 10**

Steps 1) Apply BODMAS

Step 2) Change Sign of Divide into Multiply i.e ( ÷ 10 ) convert with ( × )

Solution:

= 5005 – 5000 ×

= 5005 – 500

= 4505 Answer/-

**Question 2) Question regarding – Simplification tricks, rule, methods, solution **

** 4 **** + 3 **** + ? + 2 **** = 13 **

**Solution) **

**4 **** + 3 **** + ? + 2 **** = 13 **

**Step 1) Convert mixed fraction into simple fraction **

**i.e. mixed fraction (4 **** ) convert into ( **** ) simple fraction **

**—————————**

**Method of Conversion mixed fraction into Simple fraction**

**= 4 **** **

**= 4 + **** **

**= **** **

**= **** **

**——————————–**

** **

+ + x + =

** **

**Firstly find the value of x**

Shift these values to the right hand side ( Note: while shifting, if the values are positive before shifting, then the values become negative after shifting )

x = ** – ( ** + + )

x = ** – ( ** )

x = ** – **** **

x = ** – 10**

x = ** **

x = ** or It can also be written as 3 **

**Question 3 : **

** 1 ÷ [1 + 1 ÷ { 1 + 1 ÷ ( 1 + 1 ÷ 2 )}]**

Solution:

Apply BODMAS Rule

**Step 1) Change Sign of Divide into Multiply i.e ( ÷ 2 ) convert with ( × **** )**

= 1 ÷ [1 + 1 ÷ { 1 + 1 ÷ ( 1 + 1 × )}]

**Step 2) Start solving from the inner most bracket**

= 1 ÷ [1 + 1 ÷ { 1 + 1 ÷ ( 1 + )}]

= 1 ÷ [1 + 1 ÷ { 1 + 1 ÷ }]

= 1 ÷ [1 + 1 ÷ { 1 + 1 ÷ }]

= 1 ÷ [1 + 1 ÷ { 1 + 1 × }]

= 1 ÷ [1 + 1 ÷ { 1 + }]

= 1 ÷ [1 + 1 ÷ ]

= 1 ÷ [1 + 1 × ]

= 1 ÷ [1 + ]

= 1 ÷

= 1 ×

=

**Question 4) Question regarding – Simplification tricks, rule, methods, solution for the same.**

**A man divides Rs. 8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew and each son receives five times as much as each nephew, how much does each daughter receive?**

Solution)

In the above statement the man is sharing money between Sons, Daughters and nephew and everybody is receiving more money that nephew.

So, Let’s take the share for nephew = x

Share for each daughter = Rs. 4x (i.e. 4 times more that nephew)

Share for each son = Rs. 5x (i.e. 5 times more that nephew)

**Therefore, Total amount 8600 = 5 Sons (5x) + 4 Daughters (4x) +2 nephew (x)**

So,

8600 = 5 (5x) + 4 (4x) + 2x

8600 = 25x + 16x + 2x

8600 = 43x

= x

200 = x

Share of Daughter’s = 4x = 4 × 200 = 800

** **

**Check / Verify:**

Total amount Rs. 8600 = 5 Sons × (5 × 200) + 4 Daughters × (4× 200) +2 nephew × 200

= 5000 + 3200 + 400

= 8600