To solve \( 7 \frac{1}{9} \times \frac{6}{7} \), let's break it down step-by-step.

### Step 1: Convert the mixed number into an improper fraction
First, convert \( 7 \frac{1}{9} \) to an improper fraction:
\[
7 \frac{1}{9} = \frac{(7 \times 9) + 1}{9} = \frac{63 + 1}{9} = \frac{64}{9}
\]

### Step 2: Multiply the fractions
Now, multiply the two fractions:
\[
\frac{64}{9} \times \frac{6}{7}
\]

Multiply the numerators and the denominators:
\[
\frac{64 \times 6}{9 \times 7} = \frac{384}{63}
\]

### Step 3: Simplify the fraction
We now simplify \( \frac{384}{63} \). The greatest common divisor (GCD) of 384 and 63 is 3, so divide both numerator and denominator by 3:
\[
\frac{384 \div 3}{63 \div 3} = \frac{128}{21}
\]

Thus, the simplified product is \( \frac{128}{21} \), or as a mixed number:
\[
6 \frac{2}{21}
\]

### Final Answer:
\[
7 \frac{1}{9} \times \frac{6}{7} = 6 \frac{2}{21}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you convert a mixed number to an improper fraction?
2. How do you simplify fractions in multiplication problems?
3. What is the GCD, and how do you find it?
4. How do you convert an improper fraction back to a mixed number?
5. Can you show the same multiplication problem with decimals?

### Tip:
Always simplify fractions after multiplying to make the result easier to interpret!

Learn how to multiply the mixed number 7 1/9 by the fraction 6/7 with a detailed step-by-step solution. This problem covers key concepts such as converting mixed numbers to improper fractions, multiplying fractions, and simplifying using the GCD. Suitable for students in Grades 6-8.

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