# Tips And Tricks And Shortcuts For Numbers, Decimals And Fractions

## Tips and Tricks and Shortcuts for Number, Decimals, and Fractions:-

Here are some best tips and tricks for the Number power, decimals questions. Which will directly help in different competitive and recruitment exams.

## Number, Decimals and Fractions Tips:

#### (Must Remember)

1) (a – b)2 = (a2 + b2 – 2ab)
2) (a + b)2 = (a2 + b2 + 2ab)
3) (a + b) (a – b) = (a2 – b2 )
4) (a3 + b3) = (a + b) (a2 – ab + b2)
5) (a3 – b3) = (a – b) (a2 – ab + b2)
6) (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
7) (a3 + b3 + c3 – 3abc) = (a + b + c) (a2 + b2 + c– ab – bc – ac)

## Number, Decimals and Fractions Tips and Tricks and Shortcuts:

### Question 1

Evaluate

$\frac{(3.8^2-1.2^2)}{(3.8 +{1.2})}\$

(a) 5.2
(b) 4.8
(c) 4
(d) 5

#### Explanation :

$\frac{(3.8^2-1.2^2)}{(3.8 +{1.2})}\$
$3.8 + 1.2$$3.8 – 1.2$$( 3.8 – 1.2 )$

=(3.8+1.2)(3.81.2)(3.81.2) =3.8+1.2 =5

## Tips and Tricks and Shortcuts for Number, Decimal and Fractions.

### Question 2

If 1.5x = 0.04y, then the value of ( (y – x) / (y+x) ) is :

(a) 73/77
(b)  7.3/77
(c) 730/77
(d) 7300/77

#### Explanation:

x / y  = 0.04 / 1.5 = 4 / 150 = 2 / 75.

= > ( (y – x) / (y+x) ) = (1 – (x / y)) / ( 1 + ( x / y)) = (1 – 2/75) / (1 + 2/75) = 73/77

### Question 3.

If 47. 2506 = 4*A + 7/B + 2*C + 5/D + 6*E, then the value of 5*A + 3*B + 6*C + D + 3*E is :

(a) 53.6003
(b) 53.603
(c) 153.6003
(d) 213.003

#### Explanation:

4*A + 7/B + 2*C + 5/D + 6*E =47.2506
=> 4 * A + 7/B + 2 *C + 5/D + 6*E = 40 + 7 + 0.2 + 0.05 + 0.0006
Comparing the terms on both sides, we get :
4*A =40, 7/B = 7, 2*C = 0.2, 5/D = 0.05, 6*E = 0.0006
A = 10,
B = 1,
C = 0.1,
D = 100,
E = 0.0001.
5*A + 3*B + 6*C + D + 3*E =(5*10) + (3*1) + (6*0.1) +100 +(3*0.0001)
=50 + 3 + 0.6 + 100 + 0.003 = 153.6003.

Read Also: How to solve Number, Decimals, and Fractions question

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