Paul Used 3 4 \frac{3}{4} 4 3 Cup Of Butter In The Batch Of Brownies He Made. He Ate 1 6 \frac{1}{6} 6 1 Of The Batch Of Brownies. What Fraction Of A Cup Of Butter Did He Consume When He Ate The Brownies?

Mar 12, 2025 by ADMIN 209 views

**Fraction of Butter Consumed in Brownies**

Introduction

In this article, we will explore the concept of fractions and how they can be used to calculate the amount of butter consumed in a batch of brownies. We will use real-world examples to illustrate the application of fractions in everyday life.

Understanding Fractions

A fraction is a way to represent a part of a whole. It consists of two parts: the numerator and the denominator. The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts the whole is divided into.

Calculating the Fraction of Butter Consumed

Let's start by analyzing the situation. Paul used $\frac{3}{4}$ cup of butter in the batch of brownies he made. He then ate $\frac{1}{6}$ of the batch of brownies. To calculate the fraction of a cup of butter he consumed, we need to multiply the fraction of butter used by the fraction of the batch he ate.

Multiplying Fractions

When multiplying fractions, we multiply the numerators together and the denominators together.

\frac{3}{4} \times \frac{1}{6} = \frac{3 \times 1}{4 \times 6} = \frac{3}{24}

Simplifying the Fraction

The fraction $\frac{3}{24}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

\frac{3}{24} = \frac{3 \div 3}{24 \div 3} = \frac{1}{8}

Conclusion

In conclusion, Paul consumed $\frac{1}{8}$ cup of butter when he ate the brownies. This example illustrates the importance of fractions in real-world applications and how they can be used to calculate the amount of butter consumed in a batch of brownies.

Real-World Applications

Fractions are used in a variety of real-world applications, including cooking, science, and finance. In cooking, fractions are used to measure ingredients and calculate the amount of a particular ingredient that is needed. In science, fractions are used to represent the concentration of a solution or the amount of a particular substance that is present in a sample. In finance, fractions are used to represent the interest rate on a loan or the amount of a particular investment that is expected to return.

Examples of Fractions in Real-World Applications

In cooking, a recipe may call for $\frac{1}{2}$ cup of flour or $\frac{3}{4}$ cup of sugar.
In science, a solution may have a concentration of $\frac{1}{4}$ molar or $\frac{2}{3}$ molar.
In finance, a loan may have an interest rate of $\frac{1}{4}$ percent or $\frac{3}{4}$ percent.

Tips for Working with Fractions

When multiplying fractions, multiply the numerators together and the denominators together.
When simplifying a fraction, divide both the numerator and the denominator by their greatest common divisor.
When adding or subtracting fractions, make sure the denominators are the same.

Conclusion

In conclusion, fractions are an important concept in mathematics that has a wide range of real-world applications. By understanding how to work with fractions, we can calculate the amount of butter consumed in a batch of brownies, measure ingredients in a recipe, and represent the concentration of a solution in science. With practice and patience, anyone can become proficient in working with fractions and apply them to a variety of real-world situations.

Final Thoughts

Q: What is a fraction?

A: A fraction is a way to represent a part of a whole. It consists of two parts: the numerator and the denominator. The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts the whole is divided into.

Q: How do I multiply fractions?

A: When multiplying fractions, you multiply the numerators together and the denominators together. For example, to multiply $\frac{3}{4}$ and $\frac{1}{6}$ , you would multiply the numerators together (3 x 1) and the denominators together (4 x 6), resulting in $\frac{3 \times 1}{4 \times 6} = \frac{3}{24}$ .

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify $\frac{3}{24}$ , you would divide both the numerator and the denominator by 3, resulting in $\frac{1}{8}$ .

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way to represent a part of a whole, while a decimal is a way to represent a number as a sum of powers of 10. For example, the fraction $\frac{1}{2}$ is equal to the decimal 0.5.

Q: How do I add fractions?

A: To add fractions, you need to have the same denominator. If the denominators are different, you need to find the least common multiple (LCM) of the two denominators and convert both fractions to have that denominator. For example, to add $\frac{1}{4}$ and $\frac{1}{6}$ , you would find the LCM of 4 and 6, which is 12, and convert both fractions to have a denominator of 12.

Q: How do I subtract fractions?

A: To subtract fractions, you need to have the same denominator. If the denominators are different, you need to find the least common multiple (LCM) of the two denominators and convert both fractions to have that denominator. For example, to subtract $\frac{1}{4}$ and $\frac{1}{6}$ , you would find the LCM of 4 and 6, which is 12, and convert both fractions to have a denominator of 12.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly. For example, the LCM of 4 and 6 is 12, because both 4 and 6 can divide into 12 evenly.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator. For example, to convert $\frac{1}{2}$ to a decimal, you would divide 1 by 2, resulting in 0.5.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you need to find the greatest power of 10 that is less than or equal to the decimal. For example, to convert 0.5 to a fraction, you would find that the greatest power of 10 that is less than or equal to 0.5 is 10^(-1), and the fraction would be $\frac{5}{10}$ , which can be simplified to $\frac{1}{2}$ .

Q: What are some real-world applications of fractions?

A: Fractions have many real-world applications, including cooking, science, and finance. In cooking, fractions are used to measure ingredients and calculate the amount of a particular ingredient that is needed. In science, fractions are used to represent the concentration of a solution or the amount of a particular substance that is present in a sample. In finance, fractions are used to represent the interest rate on a loan or the amount of a particular investment that is expected to return.

Q: How can I practice working with fractions?

A: There are many ways to practice working with fractions, including:

Using online resources, such as fraction calculators and practice problems
Working with real-world examples, such as cooking and science
Practicing with flashcards or other study aids
Joining a study group or working with a tutor

Conclusion

Fractions are an important concept in mathematics that has many real-world applications. By understanding how to work with fractions, you can solve problems in cooking, science, and finance. Whether you are a student, a professional, or simply someone who enjoys cooking or science, fractions are an important concept to understand. With practice and patience, anyone can become proficient in working with fractions and apply them to a variety of real-world situations.