Carter Has 60 Balloons. \[$\frac{4}{12}\$\] Of The Balloons Are Black, And \[$\frac{3}{12}\$\] Of The Balloons Are White. The Rest Of The Balloons Are Red. How Many Red Balloons Does Carter Have? Show Your Calculations In The Space

Feb 27, 2025 by ADMIN 232 views

**Carter's Balloon Collection: A Mathematical Exploration**

Introduction

Carter has a collection of 60 balloons, each with a unique color. The balloons are divided into three categories: black, white, and red. In this article, we will explore the mathematical concept of fractions and proportions to determine the number of red balloons in Carter's collection.

The Problem

Carter has 60 balloons, and ${$ \frac{4}{12}$}$ of them are black, while ${$ \frac{3}{12}$}$ are white. The remaining balloons are red. We need to find the number of red balloons in Carter's collection.

Step 1: Calculate the Number of Black Balloons

To find the number of black balloons, we need to multiply the total number of balloons (60) by the fraction representing the black balloons ( ${$ \frac{4}{12}$}$).

${$ \frac{4}{12} \times 60 = \frac{4 \times 60}{12} = \frac{240}{12} = 20$}$

So, Carter has 20 black balloons.

Step 2: Calculate the Number of White Balloons

Similarly, to find the number of white balloons, we multiply the total number of balloons (60) by the fraction representing the white balloons ( ${$ \frac{3}{12}$}$).

${$ \frac{3}{12} \times 60 = \frac{3 \times 60}{12} = \frac{180}{12} = 15$}$

So, Carter has 15 white balloons.

Step 3: Calculate the Number of Red Balloons

Now that we have the number of black and white balloons, we can find the number of red balloons by subtracting the sum of black and white balloons from the total number of balloons.

${ $60 - (20 + 15) = 60 - 35 = 25\$}$

So, Carter has 25 red balloons.

Conclusion

In this article, we used the mathematical concept of fractions and proportions to determine the number of red balloons in Carter's collection. By multiplying the total number of balloons by the fractions representing the black and white balloons, we found that Carter has 20 black balloons and 15 white balloons. Finally, by subtracting the sum of black and white balloons from the total number of balloons, we found that Carter has 25 red balloons.

Key Takeaways

Fractions can be used to represent proportions of a whole.
Multiplying a fraction by a number gives the product of the numerator and the number, divided by the denominator.
Subtracting the sum of two or more numbers from a total number gives the difference between the total and the sum.

Real-World Applications

Understanding fractions and proportions is essential in various real-world applications, such as:

Cooking: Measuring ingredients using fractions and proportions.
Science: Understanding chemical reactions and proportions of reactants.
Finance: Calculating interest rates and proportions of investments.

Practice Problems

Try these practice problems to reinforce your understanding of fractions and proportions:

A bakery has 120 loaves of bread, and ${$ \frac{2}{5}$}$ of them are whole wheat. How many whole wheat loaves does the bakery have?
A student has 90 pencils, and ${$ \frac{3}{10}$}$ of them are colored. How many colored pencils does the student have?
A company has 180 employees, and ${$ \frac{2}{5}$}$ of them are managers. How many managers does the company have?
Carter's Balloon Collection: A Mathematical Exploration - Q&A ===========================================================

Introduction

In our previous article, we explored the mathematical concept of fractions and proportions to determine the number of red balloons in Carter's collection. We calculated that Carter has 25 red balloons. In this article, we will answer some frequently asked questions related to the problem and provide additional insights.

Q&A

Q: What is the total number of balloons in Carter's collection?

A: The total number of balloons in Carter's collection is 60.

Q: What is the fraction of black balloons in Carter's collection?

A: The fraction of black balloons in Carter's collection is ${$ \frac{4}{12}$}$.

Q: What is the fraction of white balloons in Carter's collection?

A: The fraction of white balloons in Carter's collection is ${$ \frac{3}{12}$}$.

Q: How many black balloons does Carter have?

A: Carter has 20 black balloons.

Q: How many white balloons does Carter have?

A: Carter has 15 white balloons.

Q: How many red balloons does Carter have?

A: Carter has 25 red balloons.

Q: What is the proportion of red balloons in Carter's collection?

A: The proportion of red balloons in Carter's collection is ${$ \frac{25}{60}$}$ or ${$ \frac{5}{12}$}$.

Q: How can we represent the number of red balloons as a fraction of the total number of balloons?

A: We can represent the number of red balloons as a fraction of the total number of balloons by dividing the number of red balloons (25) by the total number of balloons (60).

${$ \frac{25}{60} = \frac{5}{12}$}$

Q: What is the relationship between the fractions of black and white balloons?

A: The fractions of black and white balloons are complementary, meaning that their sum is equal to 1.

${$ \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$}$

Q: How can we use this relationship to find the number of red balloons?

A: We can use the relationship between the fractions of black and white balloons to find the number of red balloons by subtracting the sum of black and white balloons from the total number of balloons.