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Which one of the following is an equivalent fraction for 
?
?- a)5/13
- b)6/13
- c)5/6
- d)6/7
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Which one of the following is an equivalent fraction for ?a)5/13b)6/13...
Solution:
To find an equivalent fraction, we need to simplify the given fraction by dividing both the numerator and denominator by the greatest common factor (GCF) of the two numbers.
Step 1: Find the GCF of 260 and 312.
The factors of 260 are: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, and 260.
The factors of 312 are: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312.
The common factors of 260 and 312 are: 1, 2, 4, 13, and 26.
Therefore, the GCF of 260 and 312 is 26.
Step 2: Divide both the numerator and denominator by 26.
260 ÷ 26 = 10
312 ÷ 26 = 12
Therefore, the equivalent fraction is 10/12, which can be simplified further.
Step 3: Find the GCF of 10 and 12.
The factors of 10 are: 1, 2, 5, and 10.
The factors of 12 are: 1, 2, 3, 4, 6, and 12.
The common factors of 10 and 12 are: 1, 2.
Therefore, the GCF of 10 and 12 is 2.
Step 4: Divide both the numerator and denominator by 2.
10 ÷ 2 = 5
12 ÷ 2 = 6
Therefore, the simplified fraction is 5/6, which is equivalent to 260/312.
Hence, the correct answer is option C) 5/6.
To find an equivalent fraction, we need to simplify the given fraction by dividing both the numerator and denominator by the greatest common factor (GCF) of the two numbers.
Step 1: Find the GCF of 260 and 312.
The factors of 260 are: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, and 260.
The factors of 312 are: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312.
The common factors of 260 and 312 are: 1, 2, 4, 13, and 26.
Therefore, the GCF of 260 and 312 is 26.
Step 2: Divide both the numerator and denominator by 26.
260 ÷ 26 = 10
312 ÷ 26 = 12
Therefore, the equivalent fraction is 10/12, which can be simplified further.
Step 3: Find the GCF of 10 and 12.
The factors of 10 are: 1, 2, 5, and 10.
The factors of 12 are: 1, 2, 3, 4, 6, and 12.
The common factors of 10 and 12 are: 1, 2.
Therefore, the GCF of 10 and 12 is 2.
Step 4: Divide both the numerator and denominator by 2.
10 ÷ 2 = 5
12 ÷ 2 = 6
Therefore, the simplified fraction is 5/6, which is equivalent to 260/312.
Hence, the correct answer is option C) 5/6.
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Community Answer
Which one of the following is an equivalent fraction for ?a)5/13b)6/13...
The fraction can be reduced by using smaller common fractions like dividing both by 2 until one of the numbers turns into an odd number. Alternatively, the highest common factor can be found, which is 52 in this case. Dividing both by 52, we get 5/6.
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