The Population Of A Village Is In The Following Ratios:- Women : Children = $13: 4$- Men : Children = $7: 3$a) Find The Ratio Of Women : Men.Give Your Answer In Its Simplest Form.Women : Men = $\square : \square$
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Introduction
In this article, we will explore the population of a village, which is given in the form of ratios. The ratios provided are Women : Children = 13 : 4 and Men : Children = 7 : 3. Our goal is to find the ratio of Women to Men in its simplest form.
Understanding the Ratios
To begin, let's analyze the given ratios. The ratio of Women to Children is 13 : 4, and the ratio of Men to Children is 7 : 3. These ratios tell us the proportion of women and men to children in the village.
Women to Children Ratio
The ratio of Women to Children is 13 : 4. This means that for every 13 women, there are 4 children. We can represent this ratio as a fraction: 13/4.
Men to Children Ratio
The ratio of Men to Children is 7 : 3. This means that for every 7 men, there are 3 children. We can represent this ratio as a fraction: 7/3.
Finding the Ratio of Women to Men
Now that we have the ratios of Women to Children and Men to Children, we can find the ratio of Women to Men. To do this, we need to find a common term between the two ratios. In this case, the common term is Children.
Finding the Least Common Multiple (LCM)
To find the ratio of Women to Men, we need to find the least common multiple (LCM) of the denominators of the two ratios. The LCM of 4 and 3 is 12.
Converting the Ratios to Have a Common Denominator
Now that we have the LCM, we can convert the ratios to have a common denominator of 12.
- Women to Children: 13/4 = (13 × 3)/(4 × 3) = 39/12
- Men to Children: 7/3 = (7 × 4)/(3 × 4) = 28/12
Finding the Ratio of Women to Men
Now that we have the ratios with a common denominator, we can find the ratio of Women to Men. We can do this by dividing the number of women by the number of men.
Women to Men = 39/12 ÷ 28/12 = 39/28
Simplifying the Ratio
The ratio of Women to Men is 39/28. We can simplify this ratio by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 39 and 28 is 1, so the ratio cannot be simplified further.
Conclusion
In conclusion, the ratio of Women to Men in the village is 39 : 28. This is the simplest form of the ratio, and it represents the proportion of women to men in the village.
Final Answer
Women : Men = 39 : 28
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Q: What is the given ratio of Women to Children in the village?
A: The given ratio of Women to Children in the village is 13 : 4.
Q: What is the given ratio of Men to Children in the village?
A: The given ratio of Men to Children in the village is 7 : 3.
Q: How do we find the ratio of Women to Men in the village?
A: To find the ratio of Women to Men in the village, we need to find a common term between the two ratios. In this case, the common term is Children. We then convert the ratios to have a common denominator and divide the number of women by the number of men.
Q: What is the least common multiple (LCM) of the denominators of the two ratios?
A: The least common multiple (LCM) of the denominators of the two ratios is 12.
Q: How do we convert the ratios to have a common denominator of 12?
A: To convert the ratios to have a common denominator of 12, we multiply the numerator and denominator of each ratio by the necessary factor.
- Women to Children: 13/4 = (13 × 3)/(4 × 3) = 39/12
- Men to Children: 7/3 = (7 × 4)/(3 × 4) = 28/12
Q: What is the ratio of Women to Men in the village?
A: The ratio of Women to Men in the village is 39 : 28.
Q: Can the ratio of Women to Men be simplified further?
A: No, the ratio of Women to Men cannot be simplified further because the greatest common divisor (GCD) of 39 and 28 is 1.
Q: What is the significance of finding the ratio of Women to Men in the village?
A: Finding the ratio of Women to Men in the village is important because it provides valuable information about the population demographics. It can be used to make informed decisions about resource allocation, infrastructure development, and social services.
Q: How can the ratio of Women to Men be used in real-life scenarios?
A: The ratio of Women to Men can be used in various real-life scenarios, such as:
- Planning for healthcare services and facilities
- Allocating resources for education and social services
- Developing infrastructure for housing and transportation
- Making informed decisions about economic development and investment
Q: What are some potential challenges in finding the ratio of Women to Men in a village?
A: Some potential challenges in finding the ratio of Women to Men in a village include:
- Inaccurate or incomplete data
- Limited access to information
- Cultural or social barriers to data collection
- Methodological errors in data analysis
Q: How can these challenges be overcome?
A: These challenges can be overcome by:
- Using multiple data sources and methods to validate findings
- Collaborating with local communities and stakeholders to ensure accurate and reliable data
- Developing culturally sensitive and inclusive data collection methods
- Conducting thorough quality control and data analysis to ensure accuracy and reliability.