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Find a fraction, that becomes 1/2 when 2 is added to its numerator and when 1 is subtracted from its denominator, it becomes 1/3?
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Find a fraction, that becomes 1/2 when 2 is added to its numerator and...
Identifying the Given Conditions:
To find the fraction that satisfies the given conditions, we first need to identify what the conditions are:
1. When 2 is added to the numerator, the fraction becomes 1/2.
2. When 1 is subtracted from the denominator, the fraction becomes 1/3.
Solving for the Fraction:
Let's denote the fraction as x/y, where x is the numerator and y is the denominator.
Condition 1:
Adding 2 to the numerator gives us the fraction (x+2)/y = 1/2.
Condition 2:
Subtracting 1 from the denominator gives us the fraction x/(y-1) = 1/3.
Solving the Equations:
From Condition 1:
(x+2)/y = 1/2
=> 2(x+2) = y
From Condition 2:
x/(y-1) = 1/3
=> 3x = y-1
Substitute y from Condition 1 into Condition 2:
3x = 2(x+2) - 1
=> 3x = 2x + 4 - 1
=> x = 3
Find y:
y = 2(x+2) = 2(3+2) = 10
Therefore, the fraction that satisfies the given conditions is 3/10.
To find the fraction that satisfies the given conditions, we first need to identify what the conditions are:
1. When 2 is added to the numerator, the fraction becomes 1/2.
2. When 1 is subtracted from the denominator, the fraction becomes 1/3.
Solving for the Fraction:
Let's denote the fraction as x/y, where x is the numerator and y is the denominator.
Condition 1:
Adding 2 to the numerator gives us the fraction (x+2)/y = 1/2.
Condition 2:
Subtracting 1 from the denominator gives us the fraction x/(y-1) = 1/3.
Solving the Equations:
From Condition 1:
(x+2)/y = 1/2
=> 2(x+2) = y
From Condition 2:
x/(y-1) = 1/3
=> 3x = y-1
Substitute y from Condition 1 into Condition 2:
3x = 2(x+2) - 1
=> 3x = 2x + 4 - 1
=> x = 3
Find y:
y = 2(x+2) = 2(3+2) = 10
Therefore, the fraction that satisfies the given conditions is 3/10.
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Find a fraction, that becomes 1/2 when 2 is added to its numerator and when 1 is subtracted from its denominator, it becomes 1/3?
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Find a fraction, that becomes 1/2 when 2 is added to its numerator and when 1 is subtracted from its denominator, it becomes 1/3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find a fraction, that becomes 1/2 when 2 is added to its numerator and when 1 is subtracted from its denominator, it becomes 1/3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a fraction, that becomes 1/2 when 2 is added to its numerator and when 1 is subtracted from its denominator, it becomes 1/3?.
Find a fraction, that becomes 1/2 when 2 is added to its numerator and when 1 is subtracted from its denominator, it becomes 1/3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find a fraction, that becomes 1/2 when 2 is added to its numerator and when 1 is subtracted from its denominator, it becomes 1/3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a fraction, that becomes 1/2 when 2 is added to its numerator and when 1 is subtracted from its denominator, it becomes 1/3?.
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