https://file.aiquickdraw.com/mathbot/file/1729561389264csik8olx.jpg

Let's solve the first few problems from the image, which involve dividing fractions.

### Problem (a):
\[
\frac{2}{3} \div \frac{1}{5}
\]
When dividing fractions, we multiply by the reciprocal of the second fraction:
\[
\frac{2}{3} \times \frac{5}{1} = \frac{2 \times 5}{3 \times 1} = \frac{10}{3}
\]
So, the answer is:
\[
\frac{10}{3}
\]

### Problem (b):
\[
\frac{1}{4} \div \frac{2}{3}
\]
Again, multiply by the reciprocal:
\[
\frac{1}{4} \times \frac{3}{2} = \frac{1 \times 3}{4 \times 2} = \frac{3}{8}
\]
So, the answer is:
\[
\frac{3}{8}
\]

### Problem (c):
\[
\frac{4}{5} \div \frac{2}{5}
\]
Multiply by the reciprocal:
\[
\frac{4}{5} \times \frac{5}{2} = \frac{4 \times 5}{5 \times 2} = \frac{20}{10} = 2
\]
So, the answer is:
\[
2
\]

### Problem (d):
\[
\frac{2}{3} \div 4
\]
Divide by multiplying with the reciprocal of 4 (which is \(\frac{1}{4}\)):
\[
\frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12} = \frac{1}{6}
\]
So, the answer is:
\[
\frac{1}{6}
\]

### Problem (e):
\[
4 \div \frac{6}{7}
\]
Multiply by the reciprocal:
\[
4 \times \frac{7}{6} = \frac{28}{6} = \frac{14}{3}
\]
So, the answer is:
\[
\frac{14}{3}
\]

Would you like more detailed explanations or have questions about the steps?

Here are 5 related questions to explore further:
1. What is the general rule for dividing fractions?
2. How do you simplify a fraction after multiplying?
3. Can you convert improper fractions like \(\frac{10}{3}\) into mixed numbers?
4. How do you handle division when one of the numbers is a whole number?
5. What happens when you divide a fraction by a larger fraction?

**Tip:** Always remember to multiply by the reciprocal when dividing fractions!

Divide the following fractions: (a) 2/3 ÷ 1/5, (b) 1/4 ÷ 2/3, (c) 4/5 ÷ 2/5, (d) 2/3 ÷ 4, (e) 4 ÷ 6/7, (f) 8 ÷ 16/27, (g) 4/9 ÷ 6, (h) 18/25 ÷ 27, (i) 8/9 ÷ 3 1/5, (j) 3 1/7 ÷ 2 5/14.

Explore division of fractions, mixed numbers, and whole numbers with examples like 2/3 ÷ 1/5, 8 ÷ 16/27, and more. Learn how to divide fractions using the reciprocal rule and simplify results. Suitable for students in Grades 6-8.

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