Class 8 Exam > Class 8 Questions > A rational number such that it's denominator ...
Start Learning for Free
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.
Verified Answer
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.
This question is part of UPSC exam. View all Class 8 courses
Most Upvoted Answer
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.
Attention Class 8 Students!
To make sure you are not studying endlessly, EduRev has designed Class 8 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 8.
|
|
Explore Courses for Class 8 exam
|
|
Similar Class 8 Doubts
Top Courses for Class 8View all
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
Question Description
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.
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.
Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free.
Here you can find the meaning of 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 defined & explained in the simplest way possible. Besides giving the explanation of
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, a detailed solution 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 has been provided alongside types of 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 theory, EduRev gives you an
ample number of questions to practice 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 tests, examples and also practice Class 8 tests.
|
|
Explore Courses for Class 8 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily