A fraction becomes 9/11 if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes find the fraction. denominator a fraction reduces to 1.
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Answer:
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Answer:
Let the Numerator of the fraction to be identified be x
Let the Denominator of the fraction to be identified be y
Hence the fraction will be= x/y
According to the given data, we note that
If 2 is added to both numerator and denominator the fraction becomes 9/11.
In equation we can represent it as
⇒ (x + 2)/y + 2 = 9/11
On Cross multiplying ,
⇒ 11x + 22 = 9y + 18
Subtracting 22 from both sides,
⇒ 11x = 9y – 4
Dividing by 11, we get
⇒ x = 9y – 4/11 … (i)
Then, another given condition f 3 is added to both numerator and denominator it becomes 5/6,
The equation can be written as
⇒ (x+3)/y +3 = 5/6 … (ii)
On Cross multiplying ,
⇒ 6x + 18 = 5y + 15
Subtracting the value of x, we get
⇒ 6(9y – 4 )/11 + 18 = 5y + 15
Subtracting 18 from both the sides
⇒ 6(9y – 4 )/11 = 5y – 3
⇒ 54 – 24 = 55y – 33
⇒ –y = – 9
⇒ y = 9
Putting this value of y in equation (i), we get
⇒ x = 9y – 4
⇒ x = (81 – 4)/77
⇒ x = 77/11
⇒ x = 7
Answer
Hence, the fraction is 7/9.
Step-by-step explanation:
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