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We are given two ratios:

- Men : Children = 11 : 3
- Women : Children = 5 : 2

We need to find the ratio of Men to Women. To do this, we can set up the ratios in terms of a common quantity—children.

### Step 1: Express the ratios with a common number of children.
From the two ratios:

- For men, the ratio is 11:3, which means for every 11 men, there are 3 children.
- For women, the ratio is 5:2, which means for every 5 women, there are 2 children.

### Step 2: Make the number of children the same.
To compare the ratios, we need the same number of children in both ratios. The least common multiple (LCM) of 3 and 2 is 6.

- Multiply the first ratio (Men:Children = 11:3) by 2 to get:
  \[
  \text{Men:Children} = 22:6
  \]
- Multiply the second ratio (Women:Children = 5:2) by 3 to get:
  \[
  \text{Women:Children} = 15:6
  \]

### Step 3: Now compare the men to women.
Since the number of children is now the same in both ratios, we can directly compare the number of men to women:
\[
\text{Men:Women} = 22:15
\]

Thus, the ratio of men to women is \( \boxed{22:15} \).

Let me know if you need further details or explanations!

Here are 5 related questions:
1. How do you determine the least common multiple (LCM) of two numbers?
2. Can you explain how ratios are simplified?
3. What happens if we multiply or divide both parts of a ratio by the same number?
4. How can we compare two different ratios?
5. How does the concept of ratios apply in real-world situations?

**Tip:** Always express ratios in their simplest form by finding common factors between the numbers.

The population of a village is in the following ratios: men : children = 11 : 3, women : children = 5 : 2. Find the ratio men : women. Give your answer in its simplest form.

Learn how to find the ratio of men to women given two population ratios involving children. This problem covers key math concepts such as working with ratios and the least common multiple (LCM). Suitable for students in Grades 6-8.

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