https://file.aiquickdraw.com/mathbot/file/1726654359858iotdyyc4.jpg

Let's go through each of the multiplication of fractions shown in the image.

### 1st Problem:
\[
\frac{8}{9} \times \frac{2}{6}
\]
- Multiply the numerators: \(8 \times 2 = 16\)
- Multiply the denominators: \(9 \times 6 = 54\)

So, the result is:
\[
\frac{16}{54}
\]
Now, simplify the fraction. The greatest common divisor (GCD) of 16 and 54 is 2:
\[
\frac{16 \div 2}{54 \div 2} = \frac{8}{27}
\]

Thus, the simplified result is:
\[
\frac{8}{27}
\]

### 2nd Problem:
\[
\frac{15}{17} \times \frac{6}{6}
\]
- Multiply the numerators: \(15 \times 6 = 90\)
- Multiply the denominators: \(17 \times 6 = 102\)

So, the result is:
\[
\frac{90}{102}
\]
Now, simplify the fraction. The GCD of 90 and 102 is 6:
\[
\frac{90 \div 6}{102 \div 6} = \frac{15}{17}
\]

Thus, the simplified result is:
\[
\frac{15}{17}
\]

### 3rd Problem:
\[
\frac{20}{30} \times \frac{15}{20}
\]
- Multiply the numerators: \(20 \times 15 = 300\)
- Multiply the denominators: \(30 \times 20 = 600\)

So, the result is:
\[
\frac{300}{600}
\]
Now, simplify the fraction. The GCD of 300 and 600 is 300:
\[
\frac{300 \div 300}{600 \div 300} = \frac{1}{2}
\]

Thus, the simplified result is:
\[
\frac{1}{2}
\]

### Final Answers:
1. \(\frac{8}{9} \times \frac{2}{6} = \frac{8}{27}\)
2. \(\frac{15}{17} \times \frac{6}{6} = \frac{15}{17}\)
3. \(\frac{20}{30} \times \frac{15}{20} = \frac{1}{2}\)

Would you like more details or have any other questions?

#### 5 Related Questions:
1. How do you find the greatest common divisor (GCD) of two numbers?
2. What are the rules for simplifying fractions?
3. How can you multiply more than two fractions?
4. How do you solve division problems with fractions?
5. Can fractions with different numerators and denominators be multiplied directly?

#### Tip:
Always simplify your fractions at the end of your calculations for a more concise answer!

Multiplication of fractions: 8/9 x 2/6, 15/17 x 6/6, 20/30 x 15/20

Solve multiplication problems involving fractions like 8/9 x 2/6, 15/17 x 6/6, and 20/30 x 15/20. Learn the step-by-step process for multiplying numerators and denominators and simplifying the results. Suitable for students in Grades 5-7.

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