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If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction?
Most Upvoted Answer
If 2 is subtracted from the numerator and 1 is added to the denominato...
Explanation:
Given:
Let the original fraction be x/y.
Step 1: Forming the first equation
When 2 is subtracted from the numerator and 1 is added to the denominator, the fraction becomes (x-2)/(y+1).
According to the given condition, (x-2)/(y+1) = 1/2.
This gives us the first equation: (x-2)/(y+1) = 1/2.
Step 2: Forming the second equation
When 4 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes (x+4)/(y-3).
According to the given condition, (x+4)/(y-3) = 3/2.
This gives us the second equation: (x+4)/(y-3) = 3/2.
Step 3: Solving the equations
Solving the first equation, we get:
2(x-2) = y+1
2x - 4 = y + 1
2x = y + 5
y = 2x - 5
Substitute y = 2x - 5 into the second equation:
(x+4)/(2x-5-3) = 3/2
(x+4)/(2x-8) = 3/2
2(x+4) = 3(2x-8)
2x + 8 = 6x - 24
32 = 4x
x = 8
Substitute x = 8 into y = 2x - 5:
y = 2(8) - 5
y = 16 - 5
y = 11
Therefore, the fraction is 8/11.
Given:
Let the original fraction be x/y.
Step 1: Forming the first equation
When 2 is subtracted from the numerator and 1 is added to the denominator, the fraction becomes (x-2)/(y+1).
According to the given condition, (x-2)/(y+1) = 1/2.
This gives us the first equation: (x-2)/(y+1) = 1/2.
Step 2: Forming the second equation
When 4 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes (x+4)/(y-3).
According to the given condition, (x+4)/(y-3) = 3/2.
This gives us the second equation: (x+4)/(y-3) = 3/2.
Step 3: Solving the equations
Solving the first equation, we get:
2(x-2) = y+1
2x - 4 = y + 1
2x = y + 5
y = 2x - 5
Substitute y = 2x - 5 into the second equation:
(x+4)/(2x-5-3) = 3/2
(x+4)/(2x-8) = 3/2
2(x+4) = 3(2x-8)
2x + 8 = 6x - 24
32 = 4x
x = 8
Substitute x = 8 into y = 2x - 5:
y = 2(8) - 5
y = 16 - 5
y = 11
Therefore, the fraction is 8/11.
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If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction?
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If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction?.
If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2 is subtracted from the numerator and 1 is added to the denominator and a fraction became 1 / 2 but when four is added to the numerator and 3 subtracted from the denominator it became 3 / 2 then find the fraction?.
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