Question 13

2(1/2 + 1/3) = 1(2/3)

To solve the equation 2(1/2 + 1/3), we first need to simplify the expression inside the parentheses. Adding 1/2 and 1/3 gives us 5/6, and multiplying that by 2 results in 1(2/3).

A) 1(2/3)

This option is correct because when we calculate 1/2 + 1/3, we find a common denominator of 6, resulting in 3/6 + 2/6 = 5/6. Multiplying 5/6 by 2 gives us 10/6, which simplifies to 1(2/3).

B) 1(5/6)

This option is incorrect because it suggests that the entire expression evaluates to 1(5/6). However, the calculation of 2(1/2 + 1/3) results in 1(2/3), not 1(5/6).

C) 2(1/6)

This option is also incorrect. The expression does not evaluate to 2(1/6) since the simplification shows that 1/2 + 1/3 does not equal 1/6, making this choice invalid.

D) 2(5/6)

This option is incorrect as well. It misrepresents the calculation of the expression. The original expression simplifies to 1(2/3), not 2(5/6), which would imply a completely different equation.

Conclusion

The correct answer, 1(2/3), is derived from properly simplifying the expression 2(1/2 + 1/3) to yield 10/6, which simplifies to 1(2/3). All other options misinterpret the results of the calculation, demonstrating a misunderstanding of basic fraction addition and multiplication.