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Let's solve the ratio problem:

The given ratio is:

\[
A:B:C = \frac{2}{3} : \frac{1}{5} : \frac{3}{4}
\]

To simplify the ratio, we need to express all the terms with a common denominator. The denominators are 3, 5, and 4, so the least common denominator (LCD) is 60.

Now, let's convert each ratio term:

1. For \(\frac{2}{3}\):
\[
\frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60}
\]

2. For \(\frac{1}{5}\):
\[
\frac{1}{5} = \frac{1 \times 12}{5 \times 12} = \frac{12}{60}
\]

3. For \(\frac{3}{4}\):
\[
\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}
\]

Now we can express the ratio as:

\[
A:B:C = 40:12:45
\]

Thus, the simplified ratio is:

\[
\boxed{40:12:45}
\]

This corresponds to option **C** in the given choices.

Would you like more details or have any other questions? 

Here are 5 related questions to further practice:

1. How do you find the least common denominator when simplifying ratios?
2. Can ratios be simplified similarly to fractions? How?
3. What if the terms of the ratio were decimals instead of fractions?
4. How do you handle ratios with negative numbers?
5. How do ratios relate to proportions?

**Tip:** Always check if the terms in a ratio can be simplified further, just as you would with fractions.

Learn how to simplify the ratio A:B:C = 2/3 : 1/5 : 3/4 by finding a common denominator. This problem uses fraction conversion and ratio simplification, making it suitable for Grades 6-8 students.

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