Question

marcos needs to find the sum of \\(\frac{5}{6}\\) and \\(2\frac{4}{6}\\). his work is shown.
step 1: \\(\frac{5}{6} + 2\frac{4}{6} = 2\frac{4}{6} + \frac{5}{6}\\)
step 2: \\(\quad\quad\quad\quad\quad = 2\frac{4}{6} + \frac{2}{6} + \frac{4}{6}\\)
step 3: \\(\quad\quad\quad\quad\quad = 3 + \frac{4}{6}\\)
step 4: \\(\quad\quad\quad\quad\quad = 3\frac{4}{6}\\)
in which step does marcos make the first mistake?
step 1 step 2 step 3 step 4

Explanation:

Step1: Analyze Step 1

The commutative property of addition is used: $\frac{5}{6} + 2\frac{4}{6}=2\frac{4}{6}+\frac{5}{6}$, which is correct.

Step2: Analyze Step 2

We need to decompose $\frac{5}{6}$ into a sum that can be added to $2\frac{4}{6}$. But $\frac{5}{6}
eq\frac{2}{6}+\frac{4}{6}$ (since $\frac{2}{6}+\frac{4}{6}=\frac{6}{6} = 1$, not $\frac{5}{6}$). The correct decomposition should be $\frac{5}{6}=\frac{1}{6}+\frac{4}{6}$ (or other correct decompositions, but $\frac{2}{6}+\frac{4}{6}$ is wrong here). So Step 2 has a mistake.

Step3: Analyze Step 3 (assuming Step 2 was correct)

If Step 2 was correct, $2\frac{4}{6}+\frac{2}{6}+\frac{4}{6}=2 + \frac{4}{6}+\frac{2}{6}+\frac{4}{6}=2+\frac{10}{6}=2 + 1\frac{4}{6}=3\frac{4}{6}$, but since Step 2 is wrong, we focus on Step 2.

Step4: Analyze Step 4 (assuming previous steps were correct)

If previous steps were correct, $3+\frac{4}{6}=3\frac{4}{6}$, but the error starts in Step 2.

Answer:

Step 2