Jackson Compares The Number Of People In Two Cities.City A Has A Population Of 92,100 People. City B Has A Population Of 40,615 People.About How Many Times As Great Is The Population Of City A Compared To The Population Of City B? Select ALL

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Introduction

Comparing the populations of two cities can be a fascinating exercise in mathematics. In this article, we will delve into the world of ratios and proportions to determine how many times as great the population of City A is compared to the population of City B. We will use real-world data to illustrate this concept and provide a step-by-step guide on how to calculate the ratio of the two populations.

Population Data

According to the given data, City A has a population of 92,100 people, while City B has a population of 40,615 people. These numbers will serve as the basis for our comparison.

Calculating the Ratio

To determine how many times as great the population of City A is compared to the population of City B, we need to calculate the ratio of the two populations. The ratio is calculated by dividing the population of City A by the population of City B.

The Formula

The formula for calculating the ratio is:

Ratio = Population of City A ÷ Population of City B

Plugging in the Numbers

Using the given data, we can plug in the numbers into the formula:

Ratio = 92,100 ÷ 40,615

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 92,100 and 40,615 is 5.

Ratio = (92,100 ÷ 5) ÷ (40,615 ÷ 5) Ratio = 18,420 ÷ 8,123 Ratio = 2.27 (approximately)

Interpretation

The ratio of 2.27 indicates that the population of City A is approximately 2.27 times as great as the population of City B. This means that for every one person in City B, there are approximately 2.27 people in City A.

Conclusion

In conclusion, by using the ratio formula and simplifying the fraction, we have determined that the population of City A is approximately 2.27 times as great as the population of City B. This exercise in mathematics has provided us with a deeper understanding of how to compare the populations of two cities and has highlighted the importance of using ratios and proportions in real-world applications.

Real-World Applications

The concept of ratios and proportions has numerous real-world applications, including:

  • Economics: Understanding the ratio of supply and demand can help businesses make informed decisions about pricing and production.
  • Science: Calculating the ratio of two quantities can help scientists understand complex phenomena, such as the ratio of the speed of light to the speed of sound.
  • Engineering: Using ratios and proportions can help engineers design and optimize systems, such as bridges and buildings.

Tips and Tricks

When working with ratios and proportions, it's essential to remember the following tips and tricks:

  • Use the correct formula: Make sure to use the correct formula for calculating the ratio, which is the population of City A divided by the population of City B.
  • Simplify the fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  • Interpret the results: Interpret the results of the ratio calculation carefully, as it can provide valuable insights into the relationship between the two populations.

Conclusion

Q: What is the ratio of the population of City A to the population of City B?

A: The ratio of the population of City A to the population of City B is approximately 2.27. This means that for every one person in City B, there are approximately 2.27 people in City A.

Q: How do I calculate the ratio of two populations?

A: To calculate the ratio of two populations, you need to divide the population of City A by the population of City B. The formula is:

Ratio = Population of City A ÷ Population of City B

Q: What is the greatest common divisor (GCD) and why is it important?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. In the case of the population ratio, the GCD is 5. Simplifying the fraction by dividing both the numerator and the denominator by their GCD helps to make the ratio easier to understand.

Q: Can I use the ratio to compare the populations of other cities?

A: Yes, you can use the ratio to compare the populations of other cities. However, you need to make sure that the populations are measured in the same units (e.g., both in thousands or millions). Additionally, you need to consider the context of the comparison, as the ratio may not be directly applicable to other cities with different demographics or characteristics.

Q: How can I apply the concept of ratios and proportions in real-world situations?

A: The concept of ratios and proportions has numerous real-world applications, including:

  • Economics: Understanding the ratio of supply and demand can help businesses make informed decisions about pricing and production.
  • Science: Calculating the ratio of two quantities can help scientists understand complex phenomena, such as the ratio of the speed of light to the speed of sound.
  • Engineering: Using ratios and proportions can help engineers design and optimize systems, such as bridges and buildings.

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

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

  • Not simplifying the fraction: Failing to simplify the fraction can make the ratio difficult to understand and interpret.
  • Not considering the context: Failing to consider the context of the comparison can lead to incorrect conclusions.
  • Not using the correct formula: Using the wrong formula can lead to incorrect results.

Q: Can I use technology to help me calculate ratios and proportions?

A: Yes, you can use technology to help you calculate ratios and proportions. Many calculators and computer software programs have built-in functions for calculating ratios and proportions. Additionally, online tools and apps can help you visualize and understand complex ratios and proportions.

Q: How can I apply the concept of ratios and proportions in my everyday life?

A: The concept of ratios and proportions can be applied in many everyday situations, such as:

  • Cooking: Understanding the ratio of ingredients can help you create delicious meals.
  • Shopping: Understanding the ratio of prices can help you make informed purchasing decisions.
  • Travel: Understanding the ratio of distances can help you plan your trip and navigate unfamiliar territories.

Conclusion

In conclusion, the concept of ratios and proportions is a powerful tool for understanding and comparing complex quantities. By applying this concept in real-world situations, you can gain valuable insights and make informed decisions. Remember to avoid common mistakes and use technology to help you calculate ratios and proportions.