In A Health Center, 64 Children Have Been Vaccinated, Which Correspond To 16% Of The Total Community Of The Community, Which Is The Totality Of Children In The Community?

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Calculating the Total Number of Children in the Community

In a health center, 64 children have been vaccinated, which correspond to 16% of the total community of the community, which is the totality of children in the community. To find the total number of children in the community, we need to use the concept of percentages and proportions.

What is a Percentage?

A percentage is a way to express a value as a fraction of 100. In this case, 16% means 16 out of 100. To find the total number of children in the community, we need to set up a proportion using the given information.

Setting Up the Proportion

Let's say the total number of children in the community is x. We know that 64 children represent 16% of the total community. We can set up the following proportion:

64 = (16/100) × x

Solving the Proportion

To solve for x, we can multiply both sides of the equation by 100 to get rid of the fraction:

64 × 100 = 16x

6400 = 16x

Next, we can divide both sides of the equation by 16 to solve for x:

x = 6400 ÷ 16

x = 400

Conclusion

Therefore, the total number of children in the community is 400.

Understanding the Concept of Proportions

Proportions are a fundamental concept in mathematics that help us solve problems involving ratios and percentages. In this case, we used a proportion to find the total number of children in the community. By setting up a proportion and solving for the unknown variable, we were able to find the answer.

Real-World Applications of Proportions

Proportions have many real-world applications, including:

  • Finance: Proportions are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Proportions are used to calculate the concentration of substances, the rate of chemical reactions, and other scientific measurements.
  • Engineering: Proportions are used to design and optimize systems, including mechanical, electrical, and civil engineering systems.

Tips for Solving Proportions

When solving proportions, remember to:

  • Set up the proportion correctly: Make sure to set up the proportion with the correct ratio and variables.
  • Solve for the unknown variable: Use algebraic techniques to solve for the unknown variable.
  • Check your answer: Verify that your answer makes sense in the context of the problem.

Practice Problems

Try solving the following problems to practice your skills with proportions:

  • 25% of a group of 120 people is 30. How many people are in the group?
  • 12% of a group of 240 people is 28. How many people are in the group?
  • 18% of a group of 180 people is 32. How many people are in the group?

Answer Key

  • 120 people
  • 240 people
  • 180 people

Conclusion

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is a way to express a relationship between two quantities as a fraction or a ratio.

Q: How do I set up a proportion?

A: To set up a proportion, you need to identify the two ratios that are equal. You can write the proportion as a fraction or as a ratio of two quantities.

Q: What is the difference between a proportion and a ratio?

A: A ratio is a comparison of two quantities, while a proportion is a statement that two ratios are equal. For example, 2:3 is a ratio, while 2/3 = 4/6 is a proportion.

Q: How do I solve a proportion?

A: To solve a proportion, you need to find the value of one of the variables. You can do this by cross-multiplying the two ratios and solving for the unknown variable.

Q: What is cross-multiplication?

A: Cross-multiplication is a technique used to solve proportions. It involves multiplying the numerator of the first ratio by the denominator of the second ratio, and then multiplying the numerator of the second ratio by the denominator of the first ratio.

Q: How do I use proportions in real-life situations?

A: Proportions are used in a wide range of real-life situations, including finance, science, engineering, and more. For example, you can use proportions to calculate interest rates, investment returns, and other financial metrics.

Q: What are some common mistakes to avoid when working with proportions?

A: Some common mistakes to avoid when working with proportions include:

  • Not setting up the proportion correctly: Make sure to set up the proportion with the correct ratio and variables.
  • Not solving for the unknown variable: Use algebraic techniques to solve for the unknown variable.
  • Not checking your answer: Verify that your answer makes sense in the context of the problem.

Q: How can I practice solving proportions?

A: You can practice solving proportions by working through practice problems, such as those found in math textbooks or online resources. You can also try solving proportions in real-life situations, such as calculating interest rates or investment returns.

Q: What are some advanced topics related to proportions?

A: Some advanced topics related to proportions include:

  • Similar triangles: Similar triangles are triangles that have the same shape but not necessarily the same size.
  • Similar figures: Similar figures are figures that have the same shape but not necessarily the same size.
  • Proportional reasoning: Proportional reasoning is the ability to reason about proportions and ratios.

Q: How can I apply proportions to my career or personal life?

A: Proportions can be applied to a wide range of careers and personal situations, including:

  • Finance: Proportions can be used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Proportions can be used to calculate the concentration of substances, the rate of chemical reactions, and other scientific measurements.
  • Engineering: Proportions can be used to design and optimize systems, including mechanical, electrical, and civil engineering systems.

Conclusion

In conclusion, proportions are a fundamental concept in mathematics that help us solve problems involving ratios and percentages. By setting up a proportion and solving for the unknown variable, we can find the answer to a wide range of problems. Remember to set up the proportion correctly, solve for the unknown variable, and check your answer to ensure that it makes sense in the context of the problem.