Question

add the following and find the sum in simplest form:
\\(\frac{2}{3} + \frac{1}{2}\\)
(1 point)
\\(\bigcirc\\) \\(\frac{7}{6}\\)
\\(\bigcirc\\) \\(\frac{1}{3}\\)
\\(\bigcirc\\) \\(1\frac{1}{6}\\)
\\(\bigcirc\\) 1

Explanation:

Step1: Find a common denominator

The denominators are 3 and 2. The least common denominator is 6. Rewrite the fractions: $\frac{2}{3} = \frac{2\times2}{3\times2} = \frac{4}{6}$ and $\frac{1}{2} = \frac{1\times3}{2\times3} = \frac{3}{6}$.

Step2: Add the fractions

Add the numerators: $\frac{4}{6} + \frac{3}{6} = \frac{4 + 3}{6} = \frac{7}{6}$. Convert to a mixed number: $\frac{7}{6} = 1\frac{1}{6}$.

Answer:

A. $\frac{7}{6}$, C. $1\frac{1}{6}$ (Note: $\frac{7}{6}$ and $1\frac{1}{6}$ are equivalent, both are correct representations of the sum. If considering the options, both the improper fraction and mixed number forms are correct. But typically in such questions, both can be considered correct. However, if we check the options, both $\frac{7}{6}$ (first option) and $1\frac{1}{6}$ (third option) are correct as $\frac{7}{6}=1\frac{1}{6}$.)

Wait, actually, let's recheck. The problem says "find the sum in simplest form". $\frac{7}{6}$ is an improper fraction, $1\frac{1}{6}$ is a mixed number, both are in simplest form. But let's see the options:

First option: $\frac{7}{6}$

Third option: $1\frac{1}{6}$

Both are correct because $\frac{7}{6}=1\frac{1}{6}$. But maybe the question considers both. However, let's do the calculation again. $\frac{2}{3}+\frac{1}{2}=\frac{4 + 3}{6}=\frac{7}{6}=1\frac{1}{6}$. So both options A and C are correct. But maybe the intended answer is either, but let's check the options.

Wait, the options are:

1. $\frac{7}{6}$

1. $\frac{1}{3}$

1. $1\frac{1}{6}$

1. 1

So the correct answers are A. $\frac{7}{6}$ and C. $1\frac{1}{6}$ as they are equivalent. But maybe the question expects one, but mathematically both are correct. However, let's see the calculation: $\frac{2}{3}+\frac{1}{2}=\frac{4 + 3}{6}=\frac{7}{6}=1\frac{1}{6}$. So both A and C are correct. But perhaps in the context of the question, both are acceptable. But if we have to choose from the options, both A and C are correct. But maybe the system expects one, but let's confirm.

Wait, the problem says "find the sum in simplest form". $\frac{7}{6}$ is in simplest form (improper fraction), $1\frac{1}{6}$ is also in simplest form (mixed number). So both are correct. But let's check the options. So the answer is A. $\frac{7}{6}$ and C. $1\frac{1}{6}$. But maybe the question considers both, but let's see the options. So the correct options are A and C. But maybe the intended answer is C or A. Wait, let's check the calculation again. $\frac{2}{3}+\frac{1}{2}=\frac{4 + 3}{6}=\frac{7}{6}=1\frac{1}{6}$. So both are correct. But maybe the question has a typo or considers both. But according to the options, both A and C are correct. However, if we have to choose one, maybe the mixed number is more likely the intended answer as a "simplest form" in some contexts, but mathematically both are correct.

But to follow the instruction, for multiple-choice, provide the correct options. So:

A. $\frac{7}{6}$

C. $1\frac{1}{6}$

Both are correct as they represent the same value.