`6(6)/(6)xx5(1)/(3)+17(2)/(3)xx4(1)/(4)=?`

Answer

To solve the expression \( 6\frac{6}{6} \times 5\frac{1}{3} + 17\frac{2}{3} \times 4\frac{1}{4} \), we will first convert the mixed numbers into improper fractions and then perform the calculations step by step.

### Step 1: Convert mixed numbers to improper fractions

1. **Convert \( 6\frac{6}{6} \)**:
\[ 6\frac{6}{6} = 6 + \frac{6}{6} = 6 + 1 = 7 \]

2. **Convert \( 5\frac{1}{3} \)**:
\[ 5\frac{1}{3} = 5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} \]

3. **Convert \( 17\frac{2}{3} \)**:
\[ 17\frac{2}{3} = 17 + \frac{2}{3} = \frac{51}{3} + \frac{2}{3} = \frac{53}{3} \]

4. **Convert \( 4\frac{1}{4} \)**:
\[ 4\frac{1}{4} = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4} \]

### Step 2: Substitute back into the expression

Now, we can rewrite the expression:
\[ 7 \times \frac{16}{3} + \frac{53}{3} \times \frac{17}{4} \]

### Step 3: Calculate each term

1. **Calculate \( 7 \times \frac{16}{3} \)**:
\[ 7 \times \frac{16}{3} = \frac{7 \times 16}{3} = \frac{112}{3} \]

2. **Calculate \( \frac{53}{3} \times \frac{17}{4} \)**:
\[ \frac{53 \times 17}{3 \times 4} = \frac{901}{12} \]

### Step 4: Find a common denominator and add the fractions

To add \( \frac{112}{3} \) and \( \frac{901}{12} \), we need a common denominator. The least common multiple of 3 and 12 is 12.

1. **Convert \( \frac{112}{3} \) to a denominator of 12**:
\[ \frac{112}{3} = \frac{112 \times 4}{3 \times 4} = \frac{448}{12} \]

2. **Now add the two fractions**:
\[ \frac{448}{12} + \frac{901}{12} = \frac{448 + 901}{12} = \frac{1349}{12} \]

### Final Answer

Thus, the final answer is:
\[ \frac{1349}{12} \]