Tips And Tricks And Shortcuts For Numbers, Decimals And Fractions

Shortcuts for Number, Decimals, and Fractions

As we know that numbers, decimals and fractions is a very basic topic and there are multiple methods to solve them. So here are some Tips For Numbers Decimals Fractions which will directly help in different competitive and recruitment exams. Let us look at some of the short tricks . But before that it is important to remember these identities.

Tips for Number 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.

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

Formula for Numbers, Decimal and Fractions question 

Questions on Numbers Decimal And Fraction

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