The fraction halfway between 3/7 and 4/7. A. 1/8 B. 1/4 C. 1/2 D. 1/3.
The correct answer and explanation is:
Correct Answer: None of the above.
The fraction halfway between 3/7 and 4/7 is: 3/7+4/72=7/72=12\frac{3/7 + 4/7}{2} = \frac{7/7}{2} = \frac{1}{2}
So, the correct answer is D. 1/2.
300-Word Explanation:
To find the fraction halfway between two fractions, we calculate their average. The average of two numbers is the sum of the numbers divided by 2. This applies to fractions just like whole numbers.
We are given the two fractions:
- First fraction: 37\frac{3}{7}
- Second fraction: 47\frac{4}{7}
Step 1: Add the two fractions: 37+47=77=1\frac{3}{7} + \frac{4}{7} = \frac{7}{7} = 1
Step 2: Divide the sum by 2 to get the average: 12=halfway point\frac{1}{2} = \text{halfway point}
So, 12\frac{1}{2} is exactly in the middle of 37\frac{3}{7} and 47\frac{4}{7}.
Why This Works:
Fractions with the same denominator are easy to add and compare. Since both fractions have a denominator of 7, we can treat the numerators like whole numbers:
- 37\frac{3}{7} is like “3 parts out of 7”
- 47\frac{4}{7} is like “4 parts out of 7”
To find the number halfway between 3 and 4: 3+42=72=3.5\frac{3 + 4}{2} = \frac{7}{2} = 3.5
So halfway between 37\frac{3}{7} and 47\frac{4}{7} is: 3.57=12\frac{3.5}{7} = \frac{1}{2}
Conclusion:
The answer is 1/2, which matches option D. So, D is the correct choice.