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If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is
- a)Always greater than the original fraction
- b)Always less than the origional fraction
- c)Always equal to the origional fraction
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the numerator and denominator of a proper fraction are increased by...
The correct option is A.
If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is
If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is
Larger Than the original Fraction
Proper fraction has value less than one
=> Numerator < Denominator
=> N/D < 1
=> D = N + k
N/D = (D-k)/D = D/D - k/D = 1 - k/D
if the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero then
(N+a)/(D+a) = (D-k + a)/(D + a)
= (D + a)/(D + a) - k/(D + a)
= 1 - k/(D + a)
D + a > D
=> 1/(D+a) < 1/D
=> k/(D + a) < k/D
=> -k/(D + a) > -kd
=> 1 - -k/(D + a) > 1 - kd
Hence the resulting fraction is Greater than original Proper fraction
Most Upvoted Answer
If the numerator and denominator of a proper fraction are increased by...
Explanation:
To understand why the resulting fraction is always greater than the original fraction, let's consider a specific example:
Let the original fraction be $\frac{a}{b}$, where $a$ is the numerator and $b$ is the denominator.
If we increase both the numerator and denominator by the same positive quantity, let's say $x$, the resulting fraction becomes $\frac{a+x}{b+x}$.
To compare the original fraction $\frac{a}{b}$ with the resulting fraction $\frac{a+x}{b+x}$, we can cross-multiply:
$(a)(b+x) < />
ab + ax < ab="" +="" />
ax < />
Dividing both sides by x (since x is positive), we have:
a < />
This inequality tells us that the numerator of the original fraction is less than the denominator.
Since the numerator of the resulting fraction is increased by a positive quantity (x), it will be larger than the original numerator (a).
Similarly, since the denominator of the resulting fraction is increased by the same positive quantity (x), it will be larger than the original denominator (b).
Therefore, the resulting fraction $\frac{a+x}{b+x}$ will always be greater than the original fraction $\frac{a}{b}$.
Conclusion:
Hence, the correct answer is option 'A': The resulting fraction is always greater than the original fraction.
To understand why the resulting fraction is always greater than the original fraction, let's consider a specific example:
Let the original fraction be $\frac{a}{b}$, where $a$ is the numerator and $b$ is the denominator.
If we increase both the numerator and denominator by the same positive quantity, let's say $x$, the resulting fraction becomes $\frac{a+x}{b+x}$.
To compare the original fraction $\frac{a}{b}$ with the resulting fraction $\frac{a+x}{b+x}$, we can cross-multiply:
$(a)(b+x) < />
ab + ax < ab="" +="" />
ax < />
Dividing both sides by x (since x is positive), we have:
a < />
This inequality tells us that the numerator of the original fraction is less than the denominator.
Since the numerator of the resulting fraction is increased by a positive quantity (x), it will be larger than the original numerator (a).
Similarly, since the denominator of the resulting fraction is increased by the same positive quantity (x), it will be larger than the original denominator (b).
Therefore, the resulting fraction $\frac{a+x}{b+x}$ will always be greater than the original fraction $\frac{a}{b}$.
Conclusion:
Hence, the correct answer is option 'A': The resulting fraction is always greater than the original fraction.
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If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction isa)Always greater than the original fractionb)Always less than the origional fractionc)Always equal to the origional fractiond)None of theseCorrect answer is option 'A'. Can you explain this answer?
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If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction isa)Always greater than the original fractionb)Always less than the origional fractionc)Always equal to the origional fractiond)None of theseCorrect answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction isa)Always greater than the original fractionb)Always less than the origional fractionc)Always equal to the origional fractiond)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction isa)Always greater than the original fractionb)Always less than the origional fractionc)Always equal to the origional fractiond)None of theseCorrect answer is option 'A'. Can you explain this answer?.
If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction isa)Always greater than the original fractionb)Always less than the origional fractionc)Always equal to the origional fractiond)None of theseCorrect answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction isa)Always greater than the original fractionb)Always less than the origional fractionc)Always equal to the origional fractiond)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction isa)Always greater than the original fractionb)Always less than the origional fractionc)Always equal to the origional fractiond)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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