Question 14

3 1/2 - 2 1/3 = 7 5/6

To solve the expression 3 1/2 - 2 1/3, we first convert both mixed numbers to improper fractions. This results in 7/2 for 3 1/2 and 7/3 for 2 1/3. Finding a common denominator allows us to subtract these fractions and arrive at the answer of 7 5/6.

A) 8 1/6

Option A is incorrect because it suggests a total greater than the original numbers being subtracted. After performing the subtraction, the result is less than both 3 1/2 and 2 1/3, thus eliminating the possibility of this answer being correct.

B) 7 5/6

Option B is correct as it accurately represents the result of the subtraction. After converting the mixed numbers to improper fractions and finding a common denominator, the calculation yields 7 5/6, verifying it as the correct answer.

C) 6 1/6

Option C is incorrect because it does not reflect the correct result of the subtraction. The value of 6 1/6 would imply a greater reduction than what the actual subtraction of the two mixed numbers entails.

D) 5 5/6

Option D is incorrect as it underestimates the result of the subtraction. The answer of 5 5/6 does not account for the actual difference between 3 1/2 and 2 1/3, which leads to a larger value.

Conclusion

The correct answer, 7 5/6, is derived from accurately converting and subtracting the mixed numbers involved. All other options fail to provide the correct calculation, either by exceeding or falling short of the actual difference calculated through proper arithmetic procedures.