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The denominator of a rational number is greater than numerator by 3. If 3 is subtracted from the numerator and 2 is added to denominator then the new number is 1/5 . What is the original rational number?
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The denominator of a rational number is greater than numerator by 3. I...
Understanding the Problem
To find the original rational number, let's define the variables based on the information given:
- Let the numerator be x.
- Then, the denominator will be (x + 3).
Setting Up the Equation
According to the problem, if we subtract 3 from the numerator and add 2 to the denominator, the new fraction equals 1/5.
- New numerator: (x - 3)
- New denominator: (x + 3 + 2) = (x + 5)
We can set up the equation:
- (x - 3) / (x + 5) = 1/5
Cross-Multiplying
To eliminate the fraction, we cross-multiply:
- 5(x - 3) = 1(x + 5)
This simplifies to:
- 5x - 15 = x + 5
Solving for x
Now, let's isolate x:
- 5x - x = 15 + 5
- 4x = 20
- x = 5
Finding the Denominator
Now that we have the numerator:
- Numerator (x) = 5
- Denominator = x + 3 = 5 + 3 = 8
Conclusion: The Original Rational Number
The original rational number is:
- 5/8
This satisfies both conditions outlined in the problem.
To find the original rational number, let's define the variables based on the information given:
- Let the numerator be x.
- Then, the denominator will be (x + 3).
Setting Up the Equation
According to the problem, if we subtract 3 from the numerator and add 2 to the denominator, the new fraction equals 1/5.
- New numerator: (x - 3)
- New denominator: (x + 3 + 2) = (x + 5)
We can set up the equation:
- (x - 3) / (x + 5) = 1/5
Cross-Multiplying
To eliminate the fraction, we cross-multiply:
- 5(x - 3) = 1(x + 5)
This simplifies to:
- 5x - 15 = x + 5
Solving for x
Now, let's isolate x:
- 5x - x = 15 + 5
- 4x = 20
- x = 5
Finding the Denominator
Now that we have the numerator:
- Numerator (x) = 5
- Denominator = x + 3 = 5 + 3 = 8
Conclusion: The Original Rational Number
The original rational number is:
- 5/8
This satisfies both conditions outlined in the problem.
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The denominator of a rational number is greater than numerator by 3. If 3 is subtracted from the numerator and 2 is added to denominator then the new number is 1/5 . What is the original rational number?
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The denominator of a rational number is greater than numerator by 3. If 3 is subtracted from the numerator and 2 is added to denominator then the new number is 1/5 . What is the original rational number? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The denominator of a rational number is greater than numerator by 3. If 3 is subtracted from the numerator and 2 is added to denominator then the new number is 1/5 . What is the original rational number? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The denominator of a rational number is greater than numerator by 3. If 3 is subtracted from the numerator and 2 is added to denominator then the new number is 1/5 . What is the original rational number?.
The denominator of a rational number is greater than numerator by 3. If 3 is subtracted from the numerator and 2 is added to denominator then the new number is 1/5 . What is the original rational number? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The denominator of a rational number is greater than numerator by 3. If 3 is subtracted from the numerator and 2 is added to denominator then the new number is 1/5 . What is the original rational number? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The denominator of a rational number is greater than numerator by 3. If 3 is subtracted from the numerator and 2 is added to denominator then the new number is 1/5 . What is the original rational number?.
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