6. $$ 5 \frac{2}{6} \bigcirc 5 \frac{1}{3} $$

Question

UpStudy AI · Accepted Answer

It appears you're looking to perform an operation between the two mixed numbers:

$$
5 \frac{2}{6} \bigcirc 5 \frac{1}{3}
$$

Assuming the circle symbol ($$\bigcirc$$) represents **addition**, here's how you can solve the problem:

### Step 1: Simplify the Mixed Numbers

First, simplify each mixed number if possible.

1. **Simplify $$5 \frac{2}{6}$$:**
   $$
   5 \frac{2}{6} = 5 \frac{1}{3} \quad \text{(since } \frac{2}{6} = \frac{1}{3}\text{)}
   $$
   
2. **Simplify $$5 \frac{1}{3}$$:**
   $$
   5 \frac{1}{3} \quad \text{(already in simplest form)}
   $$

### Step 2: Add the Mixed Numbers

Now, add the two simplified mixed numbers:

$$
5 \frac{1}{3} + 5 \frac{1}{3}
$$

#### Method 1: Using Mixed Numbers Directly

1. **Add the whole numbers:**
   $$
   5 + 5 = 10
   $$
   
2. **Add the fractional parts:**
   $$
   \frac{1}{3} + \frac{1}{3} = \frac{2}{3}
   $$
   
3. **Combine the sums:**
   $$
   10 + \frac{2}{3} = 10 \frac{2}{3}
   $$

#### Method 2: Converting to Improper Fractions

1. **Convert each mixed number to an improper fraction:**
   $$
   5 \frac{1}{3} = \frac{16}{3}
   $$
   
2. **Add the improper fractions:**
   $$
   \frac{16}{3} + \frac{16}{3} = \frac{32}{3}
   $$
   
3. **Convert the sum back to a mixed number:**
   $$
   \frac{32}{3} = 10 \frac{2}{3}
   $$

### Final Answer

$$
5 \frac{2}{6} + 5 \frac{1}{3} = 10 \frac{2}{3}
$$
$$ 5 \frac{2}{6} + 5 \frac{1}{3} = 10 \frac{2}{3} $$

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