Converting the Difference to a Fraction

Oct 13, 2025 by miodeya.com 132 views

Introduction

In this article, we will delve into the world of mathematics, specifically comparing heights. Alec and Joe, two brothers, are eager to know how much taller Alec is compared to Joe. To determine this, we need to convert their heights from mixed fractions to decimal form and then find the difference between their heights.

Alec's Height

Alec's height is given as $6 \frac{3}{8}$ feet. To convert this mixed fraction to decimal form, we need to convert the fraction $\frac{3}{8}$ to a decimal. We can do this by dividing the numerator (3) by the denominator (8).

\frac{3}{8} = 0.375

Now, we can add the whole number part (6) to the decimal part (0.375) to get Alec's height in decimal form.

6 \frac{3}{8} = 6 + 0.375 = 6.375

Joe's Height

Joe's height is given as $5 \frac{11}{12}$ feet. To convert this mixed fraction to decimal form, we need to convert the fraction $\frac{11}{12}$ to a decimal. We can do this by dividing the numerator (11) by the denominator (12).

\frac{11}{12} = 0.9167

Now, we can add the whole number part (5) to the decimal part (0.9167) to get Joe's height in decimal form.

5 \frac{11}{12} = 5 + 0.9167 = 5.9167

Finding the Difference

Now that we have both Alec's and Joe's heights in decimal form, we can find the difference between their heights.

\text{Difference} = \text{Alec's height} - \text{Joe's height}

\text{Difference} = 6.375 - 5.9167

\text{Difference} = 0.4583

Converting the Difference to a Fraction

To convert the decimal difference to a fraction, we can divide the decimal part (0.4583) by 1.

0.4583 = \frac{4583}{10000}

Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

\text{GCD}(4583, 10000) = 1

Since the GCD is 1, the fraction is already in its simplest form.

\frac{4583}{10000} = \frac{11}{24}

Conclusion

In conclusion, Alec is $\frac{11}{24}$ foot taller than Joe. This is because we converted their heights from mixed fractions to decimal form, found the difference between their heights, and then converted the decimal difference to a fraction.

Answer

The correct answer is B. $\frac{11}{24}$ foot.

Discussion

This problem is a great example of how to compare heights using mixed fractions and decimals. It also shows how to convert decimals to fractions and vice versa. The problem requires the student to understand the concept of mixed fractions, decimals, and fractions, as well as how to perform operations with these numbers.

Real-World Application

In real life, comparing heights is a common task. For example, when buying clothes or shoes, we need to know our height to ensure a proper fit. This problem can be used to teach students how to compare heights in a real-world context.

Tips and Variations

To make the problem more challenging, you can add more complex fractions or decimals.
To make the problem easier, you can use simpler fractions or decimals.
You can also use this problem to teach students how to convert between different units of measurement, such as feet to inches or meters to centimeters.

Conclusion

Q: What is the difference between Alec's and Joe's heights?

A: The difference between Alec's and Joe's heights is $\frac{11}{24}$ foot. This is because we converted their heights from mixed fractions to decimal form, found the difference between their heights, and then converted the decimal difference to a fraction.

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

A: To convert a mixed fraction to a decimal, you need to convert the fraction part to a decimal by dividing the numerator by the denominator. Then, you can add the whole number part to the decimal part to get the final decimal value.

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

A: To convert a decimal to a fraction, you can divide the decimal part by 1 and then simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD)?

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.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can use the Euclidean algorithm or simply list the factors of each number and find the largest common factor.

Q: What is the Euclidean algorithm?

A: The Euclidean algorithm is a method for finding the greatest common divisor (GCD) of two numbers by repeatedly applying the division algorithm.

Q: How do I apply the Euclidean algorithm?

A: To apply the Euclidean algorithm, you can follow these steps:

Divide the larger number by the smaller number to get a quotient and a remainder.
Replace the larger number with the smaller number and the smaller number with the remainder.
Repeat steps 1 and 2 until the remainder is 0.
The last non-zero remainder is the GCD.

Q: What are some real-world applications of comparing heights?

A: Comparing heights is a common task in real life, such as when buying clothes or shoes, or when measuring the height of a building or a tree.

Q: How can I make comparing heights more challenging?

A: You can make comparing heights more challenging by using more complex fractions or decimals, or by adding more variables to the problem.

Q: How can I make comparing heights easier?

A: You can make comparing heights easier by using simpler fractions or decimals, or by breaking down the problem into smaller steps.

Q: What are some tips for teaching students about comparing heights?

A: Some tips for teaching students about comparing heights include:

Using real-world examples to illustrate the concept.
Breaking down the problem into smaller steps.
Using visual aids such as diagrams or charts to help students understand the concept.
Encouraging students to work in pairs or groups to practice comparing heights.

Q: What are some variations of the comparing heights problem?

A: Some variations of the comparing heights problem include:

Comparing heights in different units of measurement, such as feet to inches or meters to centimeters.
Comparing heights of objects with different shapes or sizes.
Comparing heights of objects in different environments, such as on land or in water.

Conclusion

In conclusion, comparing heights is a fun and easy problem that can be used to teach students about mixed fractions, decimals, and fractions. By following the steps outlined in this article, students can learn how to compare heights and convert between different units of measurement.