Final answer:
The incorrect claim was that 2/3 + 1/2(8+ 3(1/4)) simplifies to 13(1/8). The correct simplification involves converting fractions to a common denominator and simplifying to get 78/24, which reduces to 3 1/4
Step-by-step explanation:
The correct value of the expression 2/3 + 1/2(8+ 3(1/4)) is found through a series of steps that require finding a common denominator, distributing multiplication over addition, and simplifying fractions. First, simplify the innermost expression, which is 3(1/4), to get 3/4. Adding this to 8 gives 8 3/4, which is equal to 35/4 when written as an improper fraction.
Next, multiply this fraction by 1/2, which gives us 35/8. Finally, we add 2/3 to 35/8 by converting 2/3 to a fraction with a denominator of 8, which is 16/24, and then the common denominator for 2/3 and 35/8 is 24. Add the converted fraction to 35/8 to get the correct simplified result, which is not 13(1/8) as Josiah claimed, but actually 78/24 or 3 1/4.