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= 25/2 + 37/3 + 73/6
= (75 + 74 + 73)/6
= 222/6
= 37
⇒ 59/20
7/9 of the people present in a hall are sitting in 9/13 of the chairs available and the rest are standing. If there are 28 empty chairs, how many chairs would have been still empty if everyone in the hall was sitting?
Let the number of people be x and number of the chair be y.
Number of available chair = y × (9/13) = 9y/13
Number of empty chair = y  (9y/13) = 4y/13
Given, Number of empty chairs = 28
According to the question
4y/13 = 28
y = 28 × (13/4) = 91
Total number of chairs = 91
Number of chairs in which people are sitting = 91  28 = 63
Number of people who sit = x × (7/9) = 7x/9
According to the question
7x/9 = 63
x = 63 × (9/7) = 81
Total number of people are = 81
Chairs would have been still empty if everyone in the hall was sitting = 91  81 = 10
Given:
The fractions are 13/19, 25/ 31, 28/31, 70/79.
Calculation:
The values are
13/19 = 0.68
25/31 = 0.80
28/31 = 0.90
70/79 = 0.88
∴ Option C is correct.
We have to find the simplified value of
Concept Used:
Concept of rationalisation: When an irrational number came in denominator in a fraction then it become difficult in calculation. To avoid this problem we multiply something with both numerator and denominator so that the denominator part become rational. This process is known as rationalisation.
In general, the process to make an irrational number to a rational number is called rationalisation.
a^{2}  b^{2} = (a + b)(a  b)
⇒ (√2  1) + (√3  √2) + (√4  √3) + ... + (√100  √99)
⇒  1 + √100
⇒ 10  1
⇒ 9
To convert a recurring decimal into a fraction For numerator write the number formed by all digits after the decimal then subtract the number without a bar(a number which is not repeated) after the decimal and for its denominator. The number is formed by as many nines as there are recurring digits repeated, followed by as many zeros as the number of nonrepeating or nonrecurring digits.
= (541  5)/990
⇒ = 536/990
∴ The required fraction is 536/990
∴ 995
⇒ 176 + 11/11
⇒ 176 + 1 = 177
∴ 177
Given expression is
⇒
⇒ 5/8
∴ The value of Expression is 5/8.
Note: Simplify using BODMAS: Bracket – Of – Division – Multiplication – Addition – Subtraction
Given:
x + 1/x = 99
Calculation:
Divide by ‘x’ in numerator and denominator both, we get
⇒ 300/300 = 1
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