Simplify 23÷49\frac{2}{3} \div \frac{4}{9}32÷94.

Let's break down and simplify the expression:

\[
23 \div 49\frac{2}{3} \div \frac{4}{9}32 \div 94
\]

We have to first deal with the mixed fraction \(49\frac{2}{3}\), rewrite it as an improper fraction.

### Step 1: Convert \(49\frac{2}{3}\) to an improper fraction.

\[
49 \frac{2}{3} = \frac{3 \times 49 + 2}{3} = \frac{147 + 2}{3} = \frac{149}{3}
\]

### Step 2: Reorganize the expression.

The expression now becomes:

\[
23 \div \frac{149}{3} \div \frac{4}{9} \times 32 \div 94
\]

### Step 3: Simplify the first part \(23 \div \frac{149}{3}\).

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
23 \div \frac{149}{3} = 23 \times \frac{3}{149} = \frac{69}{149}
\]

### Step 4: Simplify the second part \(\frac{69}{149} \div \frac{4}{9}\).

Again, dividing by a fraction means multiplying by its reciprocal:

\[
\frac{69}{149} \div \frac{4}{9} = \frac{69}{149} \times \frac{9}{4} = \frac{69 \times 9}{149 \times 4} = \frac{621}{596}
\]

### Step 5: Multiply the result by \(32 \div 94\).

First, simplify \(32 \div 94\):

\[
32 \div 94 = \frac{32}{94} = \frac{16}{47}
\]

Now, multiply:

\[
\frac{621}{596} \times \frac{16}{47} = \frac{621 \times 16}{596 \times 47} = \frac{9936}{28012}
\]

### Step 6: Simplify the final fraction.

The greatest common divisor (GCD) of 9936 and 28012 is 4. So, divide both the numerator and the denominator by 4:

\[
\frac{9936}{28012} = \frac{2484}{7003}
\]

Thus, the simplified expression is:

\[
\boxed{\frac{2484}{7003}}
\]

Would you like to see any details or ask further questions?

Here are 5 related questions you could explore:
1. How do you multiply and divide fractions?
2. How do you convert mixed numbers to improper fractions?
3. What is the GCD and how is it used to simplify fractions?
4. How can you simplify complex fractions step by step?
5. What is the process for simplifying large numbers in fractions?

**Tip:** Always remember, when dividing by a fraction, multiply by its reciprocal to simplify the process!

Learn how to simplify the expression 23 ÷ 49 2/3 ÷ 4/9 × 32 ÷ 94 with a detailed step-by-step solution. This problem covers important concepts like converting mixed numbers to improper fractions, dividing by fractions using reciprocals, and simplifying fractions using the GCD method. Suitable for Grades 7-9.

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