Tips And Tricks And Shortcuts For Numbers, Decimals And Fractions

Tips For Numbers Decimals Fractions

1) (a – b)^{2} = (a^{2} + b^{2} – 2ab)
2) (a + b)^{2} = (a^{2} + b^{2} + 2ab)
3) (a + b) (a – b) = (a^{2} – b^{2} )
4) (a^{3} + b^{3}) = (a + b) (a^{2} – ab + b^{2})
5) (a^{3} – b^{3}) = (a – b) (a^{2} – ab + b^{2})
6) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (ab + bc + ca)
7) (a^{3} + b^{3} + c^{3} – 3abc) = (a + b + c) (a^{2}+ b^{2} + c^{2} – ab – bc – ac)

Now let us look at some of the Tips For Numbers Decimals Fractions through the given examples.

Question 1 Evaluate \frac{(3.8^2-1.2^2)}{(3.8 -{1.2})}\

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

Answer : D

Explanation :

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

= 3.8+1.2 =5

Question 2 If 1.5x = 0.04y, then the value of \frac { (y – x)}{ (y+x) } is :

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

Answer: A

Explanation:

\frac{ (x)}{ (y) }

= \frac{ (0.04)}{ (1.5) }

= \frac{ (4)}{ (150) }

= \frac{ (2)}{ (75) }

= > \frac{ (y – x)}{ (y+x) } 

= \frac{(1 – \frac{x}{y})} {( 1 + \frac{x}{y})}  

= \frac {1 – \frac{2}{75}}{1 – \frac{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

Answer: C

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.

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