Class 5 Exam > Class 5 Questions > The sum of the numerator and the denominator ...
Start Learning for Free
The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?
- a)21/ 36
- b)12 / 46
- c)21 / 46
- d)12 / 36
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The sum of the numerator and the denominator of a fraction is 67. When...
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the original fraction is a/b, where a is the numerator and b is the denominator.
1. The sum of the numerator and the denominator is 67.
a + b = 67
2. When 31 is added to the denominator, the fraction becomes 3/11.
a / (b + 31) = 3/11
Now we can solve these equations.
1. Rearrange the first equation to express a in terms of b:
a = 67 - b
2. Substitute this expression for a in the second equation:
(67 - b) / (b + 31) = 3/11
3. Cross-multiply to get rid of the fractions:
11(67 - b) = 3(b + 31)
4. Expand and simplify:
737 - 11b = 3b + 93
5. Move all the b terms to one side and the constant terms to the other side:
737 - 93 = 3b + 11b
644 = 14b
6. Divide both sides by 14 to solve for b:
b = 644 / 14
b = 46
Now that we have the value of b, we can substitute it back into the first equation to solve for a:
a + 46 = 67
a = 67 - 46
a = 21
Therefore, the original fraction is 21/46, which matches option C.
Let's assume the original fraction is a/b, where a is the numerator and b is the denominator.
1. The sum of the numerator and the denominator is 67.
a + b = 67
2. When 31 is added to the denominator, the fraction becomes 3/11.
a / (b + 31) = 3/11
Now we can solve these equations.
1. Rearrange the first equation to express a in terms of b:
a = 67 - b
2. Substitute this expression for a in the second equation:
(67 - b) / (b + 31) = 3/11
3. Cross-multiply to get rid of the fractions:
11(67 - b) = 3(b + 31)
4. Expand and simplify:
737 - 11b = 3b + 93
5. Move all the b terms to one side and the constant terms to the other side:
737 - 93 = 3b + 11b
644 = 14b
6. Divide both sides by 14 to solve for b:
b = 644 / 14
b = 46
Now that we have the value of b, we can substitute it back into the first equation to solve for a:
a + 46 = 67
a = 67 - 46
a = 21
Therefore, the original fraction is 21/46, which matches option C.
Free Test
FREE
| Start Free Test |
Community Answer
The sum of the numerator and the denominator of a fraction is 67. When...
Numerator + Denominator = 67
After adding 31 to the denominator, the numerator is 3 units and denominator is 11 units.
3 + 11 = 14 units = 67 + 31 = 98
∴ 1 unit = 98 ÷ 14 = 7
3 units = 3 × 7 = 21 and 11 units = 11 × 7 = 77
New fraction = 21 / 77
Hence, the original fraction
After adding 31 to the denominator, the numerator is 3 units and denominator is 11 units.
3 + 11 = 14 units = 67 + 31 = 98
∴ 1 unit = 98 ÷ 14 = 7
3 units = 3 × 7 = 21 and 11 units = 11 × 7 = 77
New fraction = 21 / 77
Hence, the original fraction
Attention Class 5 Students!
To make sure you are not studying endlessly, EduRev has designed Class 5 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 5.
|
Explore Courses for Class 5 exam
|
|
Similar Class 5 Doubts
Top Courses for Class 5View all
The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer?
Question Description
The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer?.
The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer?.
Solutions for The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 5.
Download more important topics, notes, lectures and mock test series for Class 5 Exam by signing up for free.
Here you can find the meaning of The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 5 tests.
|
|
Explore Courses for Class 5 exam
|
|
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 to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup