Question 30

5 1/3 + 3 1/2 = 8 5/6

When adding the fractions, 5 1/3 can be converted to an improper fraction as 16/3, and 3 1/2 can be converted to 7/2. Finding a common denominator of 6 allows us to combine these fractions, resulting in a sum of 53/6, which simplifies to 8 5/6.

A) 8 2/6

This answer is incorrect because it simplifies to 8 1/3, which does not represent the correct sum of 5 1/3 and 3 1/2. The addition of the two mixed numbers yields a larger value than this option.

B) 9 1/4

This option is also incorrect. The sum of 5 1/3 and 3 1/2 is less than 9, making this option too high. The calculation confirms that the correct sum is below 9.

C) 8 2/5

This answer is incorrect. While it is close to the correct sum, 8 2/5 is equivalent to 8.4, which does not accurately reflect the sum of 5 1/3 and 3 1/2. The correct value is greater than this.

D) 8 5/6

This is the correct answer. The proper calculation of 5 1/3 and 3 1/2 results in 53/6, which equals 8 5/6 when simplified. This option accurately represents the total of the two mixed numbers.

Conclusion

The correct answer is 8 5/6, as it accurately reflects the sum of the two mixed numbers given in the problem. All other options do not match the calculated value, either being too low or too high, confirming that they are incorrect. Thus, option D is the only viable solution.