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Important Formulae

1.'BODMAS' Rule:
This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of given expression.
Here B - Bracket,
O - of,
D - Division,
M - Multiplication,
S - Subtraction
Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order (), {} and [ ].
After removing the brackets, we must use the following operations strictly in the order:
(i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.

2. Modulus of a Real Number:
Modulus of a real number a is defined as
|a| = a, if a > 0
-a, if a < 0
Thus, |5| = 5 and |-5| = -(-5) = 5.

3. Virnaculum (or Bar):
When an expression contains Virnaculum, before applying the 'BODMAS' rule, we simplify the expression under the Virnaculum.

Practice Questions

1.

 Simplify: 5005 - 5000 ÷ 10 A.4505 B.4605 C.4705 D.4805

Let, 5005 – 5000/10 = 5005 – 500 = 4505

2.

 Simplify: 343 ÷ 49 ÷ 7 ÷ 7 A.1/12 B.1/13 C.1/7 D.1/9

Let , 343 x 1/49 x 1/7 x 1/7 = 1/7

3.

 The value of 1001 ÷ 11 of 13 is : A.8 B.5 C.6 D.7

⇒ 1001 ÷ 11 x 13
⇒ 1001/(11 x 13) = 7.

4.

 The value of 25 – 5 [2 + 3 {2 – 2 (5 – 3) + 5} – 10] ÷ 4 is: A.22.25 B.23.75 C.23.25 D.22.75

⇒ 25 – 5 [2 + 3 {2 – 2 (5 – 3) + 5} – 10] ÷ 4
⇒ 25 – 5 [2 + 3 {2 – 2 x 2 + 5} – 10] ÷ 4
⇒ 25 – 5 [2 + 3 {2 – 4 + 5} – 10] ÷ 4
⇒ 25 – 5 [2 + 3 {3} – 10] ÷ 4 = 25 – 5 [2 + 9 – 10] ÷ 4
⇒ 25 – 5 ÷ 4
⇒ 25 – 1.25 = 23.75

5.

 What mathematical operation should come at the place of ‘?’ in the equation: 2 ? 6 – 12 ÷ 4 + 2 = 11 A.+ B.- C./ D.x

⇒ 2 ? 6 – 12 ÷ 4 + 2 = 11
⇒ 2 X 6 – 12 ÷ 4 + 2 = 11
⇒ 2 X 6 – 3 + 2 = 11 = 2 X 6 = 11 +3 -2
⇒ 2 X 6 = 12
So, in place of X, we apply x(multiply)

6.

 The value of [(6 + 6 + 6 + 6) ÷ 6]/(4 + 4 + 4 + 4 ÷ 4) is equal to ? A.13/4 B.4/13 C.9/4 D.4/9

⇒ (24 ÷ 6)/(4 + 4 + 4 + 1) = 4/13

7.

 Evaluate: [8 - {5 - ( - 3 + 2)} ÷ 2]/[(5 - 3) - (6 - 3) ÷3] A.3 B.4 C.5 D.6

⇒ [8 - {5 - ( - 3 + 2)} ÷ 2]/[(5 - 3) - (6 - 3) ÷3] = [8 - {5 - (-1)} ÷2]/[2 - 3 ÷3]
⇒ (8 - 6 ÷ 2)/( 2 - 1) = 8 – 3 = 5

8.

 If 1/3 + 1/2 + 1/X = 4, then X = ? A.6 / 19 B.19 / 6 C.5 / 19 D.19 / 5

1/3 + 1/2 + 1/X = 4
⇒ 1/X = 4 - 1/3 - 1/2
⇒ 1/X = (24 - 2 - 3)/6 = 19/6
⇒ X = 6/19