Performed the indicated operation and reduce the answer to lowest term(5/6×5/9) ÷1/7 and type an integer or a simplified fraction

Let's perform the indicated operation and reduce the answer to its lowest terms.

We have the expression:

\[
\left(\frac{5}{6} \times \frac{5}{9}\right) \div \frac{1}{7}
\]

### Step 1: Multiply the fractions
First, multiply \(\frac{5}{6}\) and \(\frac{5}{9}\):

\[
\frac{5}{6} \times \frac{5}{9} = \frac{5 \times 5}{6 \times 9} = \frac{25}{54}
\]

### Step 2: Divide by the second fraction
Now, divide \(\frac{25}{54}\) by \(\frac{1}{7}\). Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{25}{54} \div \frac{1}{7} = \frac{25}{54} \times \frac{7}{1} = \frac{25 \times 7}{54 \times 1} = \frac{175}{54}
\]

### Step 3: Simplify the fraction (if possible)
Check if \(\frac{175}{54}\) can be simplified further. The greatest common divisor (GCD) of 175 and 54 is 1, so the fraction is already in its simplest form.

The final answer is:

\[
\boxed{\frac{175}{54}}
\]

Would you like more details or have any questions? 

Here are 5 related questions:

1. How do you multiply fractions with different denominators?
2. What does it mean to divide one fraction by another?
3. How can you determine if a fraction can be simplified?
4. What is the reciprocal of a fraction and how is it used?
5. Why is it important to simplify fractions to their lowest terms?

**Tip:** When multiplying fractions, simply multiply the numerators together and the denominators together. Always simplify the result if possible.

Explore how to simplify the expression (5/6 × 5/9) ÷ 1/7 step-by-step with detailed explanations and examples. Learn about multiplying fractions, dividing fractions, and reducing fractions to lowest terms. Suitable for Grades 5-6.

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