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In a fraction,twice the numerator is 2 more than the denominator. if 3 is added to the numerator and denominator, the new fraction is ²/³. find the original fraction.?
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In a fraction,twice the numerator is 2 more than the denominator. if 3...
Given Information:
- Let the original fraction be $\frac{x}{y}$, where x is the numerator and y is the denominator.
- Twice the numerator is 2 more than the denominator, meaning 2x = y + 2.
- When 3 is added to both the numerator and denominator, the new fraction is $\frac{2}{3}$.
Solving the Equations:
- From the first condition, 2x = y + 2, we can rewrite this as y = 2x - 2.
- When 3 is added to both x and y, the new fraction becomes $\frac{x + 3}{y + 3}$.
- According to the second condition, the new fraction $\frac{x + 3}{y + 3}$ is equal to $\frac{2}{3}$.
Substitute and Solve:
- Substitute y = 2x - 2 into the new fraction equation: $\frac{x + 3}{2x - 2 + 3} = \frac{2}{3}$.
- Simplify the equation and solve for x: $\frac{x + 3}{2x + 1} = \frac{2}{3}$.
- Cross multiply to get 3(x + 3) = 2(2x + 1).
- Solve the equation to find x = 5.
Find the Original Fraction:
- Substitute x = 5 back into the original fraction: $\frac{5}{2(5) - 2}$.
- Simplify to get the original fraction: $\frac{5}{8}$.
Therefore, the original fraction is $\frac{5}{8}$.
- Let the original fraction be $\frac{x}{y}$, where x is the numerator and y is the denominator.
- Twice the numerator is 2 more than the denominator, meaning 2x = y + 2.
- When 3 is added to both the numerator and denominator, the new fraction is $\frac{2}{3}$.
Solving the Equations:
- From the first condition, 2x = y + 2, we can rewrite this as y = 2x - 2.
- When 3 is added to both x and y, the new fraction becomes $\frac{x + 3}{y + 3}$.
- According to the second condition, the new fraction $\frac{x + 3}{y + 3}$ is equal to $\frac{2}{3}$.
Substitute and Solve:
- Substitute y = 2x - 2 into the new fraction equation: $\frac{x + 3}{2x - 2 + 3} = \frac{2}{3}$.
- Simplify the equation and solve for x: $\frac{x + 3}{2x + 1} = \frac{2}{3}$.
- Cross multiply to get 3(x + 3) = 2(2x + 1).
- Solve the equation to find x = 5.
Find the Original Fraction:
- Substitute x = 5 back into the original fraction: $\frac{5}{2(5) - 2}$.
- Simplify to get the original fraction: $\frac{5}{8}$.
Therefore, the original fraction is $\frac{5}{8}$.
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In a fraction,twice the numerator is 2 more than the denominator. if 3 is added to the numerator and denominator, the new fraction is ²/³. find the original fraction.?
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In a fraction,twice the numerator is 2 more than the denominator. if 3 is added to the numerator and denominator, the new fraction is ²/³. find the original fraction.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In a fraction,twice the numerator is 2 more than the denominator. if 3 is added to the numerator and denominator, the new fraction is ²/³. find the original fraction.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a fraction,twice the numerator is 2 more than the denominator. if 3 is added to the numerator and denominator, the new fraction is ²/³. find the original fraction.?.
In a fraction,twice the numerator is 2 more than the denominator. if 3 is added to the numerator and denominator, the new fraction is ²/³. find the original fraction.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In a fraction,twice the numerator is 2 more than the denominator. if 3 is added to the numerator and denominator, the new fraction is ²/³. find the original fraction.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a fraction,twice the numerator is 2 more than the denominator. if 3 is added to the numerator and denominator, the new fraction is ²/³. find the original fraction.?.
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