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A rational number such that it's denominator is greater than its numerator by a constant K (K≠0). if the denominator is doubled the number obtained is again equal to original number. Find the rational number.
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A rational number such that it's denominator is greater than its numer...
Let the numerator be x .
Denominator = x+K.
Now, as per the question,
x/2(x+K) = x/(x+K)
i.e. x/2 = x =>x = 2x
which means x = 0.
So, the rational number will 0/(0+K) i.e. 0/K,where K is any constant.
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A rational number such that it's denominator is greater than its numer...
Problem: Finding the rational number
Given conditions:
- The denominator of the rational number is greater than its numerator by a constant K (K≠0).
- If the denominator is doubled, the resulting number is equal to the original number.
Step 1: Understanding the problem
Let's assume the rational number as x/y, where x is the numerator and y is the denominator. According to the first condition, we can write the equation as:
y = x + K
The second condition states that if we double the denominator, the resulting number is equal to the original number. Mathematically, we can write this as:
x/y = x/(2y)
Step 2: Solving the equations
To find the rational number, we need to solve the above two equations simultaneously. Substituting the value of y from the first equation into the second equation, we get:
x/(x + K) = x/(2(x + K))
Cross-multiplying and simplifying, we have:
2(x + K) = x
Expanding the left side:
2x + 2K = x
Moving all the terms to one side:
2x - x = -2K
Simplifying further:
x = -2K
Substituting this value of x into the first equation:
y = -2K + K
y = -K
Step 3: Final solution
Therefore, the rational number is -2K/(-K), which simplifies to 2. So, the rational number is 2.
Hence, the solution to the problem is a rational number equal to 2.
Given conditions:
- The denominator of the rational number is greater than its numerator by a constant K (K≠0).
- If the denominator is doubled, the resulting number is equal to the original number.
Step 1: Understanding the problem
Let's assume the rational number as x/y, where x is the numerator and y is the denominator. According to the first condition, we can write the equation as:
y = x + K
The second condition states that if we double the denominator, the resulting number is equal to the original number. Mathematically, we can write this as:
x/y = x/(2y)
Step 2: Solving the equations
To find the rational number, we need to solve the above two equations simultaneously. Substituting the value of y from the first equation into the second equation, we get:
x/(x + K) = x/(2(x + K))
Cross-multiplying and simplifying, we have:
2(x + K) = x
Expanding the left side:
2x + 2K = x
Moving all the terms to one side:
2x - x = -2K
Simplifying further:
x = -2K
Substituting this value of x into the first equation:
y = -2K + K
y = -K
Step 3: Final solution
Therefore, the rational number is -2K/(-K), which simplifies to 2. So, the rational number is 2.
Hence, the solution to the problem is a rational number equal to 2.
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A rational number such that it's denominator is greater than its numerator by a constant K (K≠0). if the denominator is doubled the number obtained is again equal to original number. Find the rational number. Related: NCERT Solution (Ex - 2.4) - Chapter 2: Linear Equations in one variable, Maths, Class 8
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A rational number such that it's denominator is greater than its numerator by a constant K (K≠0). if the denominator is doubled the number obtained is again equal to original number. Find the rational number. Related: NCERT Solution (Ex - 2.4) - Chapter 2: Linear Equations in one variable, Maths, Class 8 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 A rational number such that it's denominator is greater than its numerator by a constant K (K≠0). if the denominator is doubled the number obtained is again equal to original number. Find the rational number. Related: NCERT Solution (Ex - 2.4) - Chapter 2: Linear Equations in one variable, Maths, Class 8 covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rational number such that it's denominator is greater than its numerator by a constant K (K≠0). if the denominator is doubled the number obtained is again equal to original number. Find the rational number. Related: NCERT Solution (Ex - 2.4) - Chapter 2: Linear Equations in one variable, Maths, Class 8.
Solutions for A rational number such that it's denominator is greater than its numerator by a constant K (K≠0). if the denominator is doubled the number obtained is again equal to original number. Find the rational number. Related: NCERT Solution (Ex - 2.4) - Chapter 2: Linear Equations in one variable, Maths, Class 8 in English & in Hindi are available as part of our courses for Class 8.
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