Finding the Difference in Height

Oct 13, 2025 by magicalceylontours.com 128 views

Introduction

In the world of art, sculptures can be a beautiful representation of creativity and skill. However, when it comes to comparing the heights of two sculptures, mathematical calculations come into play. In this article, we will explore the problem of comparing the heights of two sculptures, Natasha's and Maya's, and determine how much shorter Natasha's sculpture was than Maya's.

Understanding the Problem

Natasha's sculpture was $$5 \frac{3}{16}$$ inches tall. Maya's sculpture was 4 times as tall as Natasha's. To find out how much shorter Natasha's sculpture was than Maya's, we need to calculate the height of Maya's sculpture and then subtract the height of Natasha's sculpture from it.

Calculating the Height of Maya's Sculpture

Since Maya's sculpture was 4 times as tall as Natasha's, we can calculate its height by multiplying Natasha's height by 4.

\text{Height of Maya's sculpture} = 4 \times \text{Height of Natasha's sculpture}

\text{Height of Maya's sculpture} = 4 \times \left(5 \frac{3}{16}\right)

To multiply a mixed number by a whole number, we can convert the mixed number to an improper fraction.

\left(5 \frac{3}{16}\right) = \frac{5 \times 16 + 3}{16} = \frac{83}{16}

Now, we can multiply the improper fraction by 4.

\text{Height of Maya's sculpture} = 4 \times \frac{83}{16}

\text{Height of Maya's sculpture} = \frac{4 \times 83}{16}

\text{Height of Maya's sculpture} = \frac{332}{16}

\text{Height of Maya's sculpture} = 20 \frac{12}{16}

\text{Height of Maya's sculpture} = 20 \frac{3}{4}

Finding the Difference in Height

Now that we have the height of Maya's sculpture, we can find the difference in height between the two sculptures by subtracting Natasha's height from Maya's height.

\text{Difference in height} = \text{Height of Maya's sculpture} - \text{Height of Natasha's sculpture}

\text{Difference in height} = 20 \frac{3}{4} - 5 \frac{3}{16}

To subtract mixed numbers, we can convert them to improper fractions.

20 \frac{3}{4} = \frac{20 \times 4 + 3}{4} = \frac{83}{4}

5 \frac{3}{16} = \frac{5 \times 16 + 3}{16} = \frac{83}{16}

Now, we can subtract the two improper fractions.

\text{Difference in height} = \frac{83}{4} - \frac{83}{16}

To subtract fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 4 and 16 is 16.

\text{Difference in height} = \frac{83 \times 4}{4 \times 4} - \frac{83}{16}

\text{Difference in height} = \frac{332}{16} - \frac{83}{16}

\text{Difference in height} = \frac{332 - 83}{16}

\text{Difference in height} = \frac{249}{16}

\text{Difference in height} = 15 \frac{9}{16}

Conclusion

In conclusion, Natasha's sculpture was $$5 \frac{3}{16}$$ inches tall, while Maya's sculpture was 4 times as tall, at $$20 \frac{3}{4}$$ inches. The difference in height between the two sculptures was $$15 \frac{9}{16}$$ inches, with Maya's sculpture being significantly taller than Natasha's.

Final Answer

Introduction

In our previous article, we explored the problem of comparing the heights of two sculptures, Natasha's and Maya's. We calculated that Maya's sculpture was $$20 \frac{3}{4}$$ inches tall, while Natasha's sculpture was $$5 \frac{3}{16}$$ inches tall. The difference in height between the two sculptures was $$15 \frac{9}{16}$$ inches. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the height of Natasha's sculpture?

A: Natasha's sculpture is $$5 \frac{3}{16}$$ inches tall.

Q: What is the height of Maya's sculpture?

A: Maya's sculpture is $$20 \frac{3}{4}$$ inches tall.

Q: How much taller is Maya's sculpture than Natasha's?

A: Maya's sculpture is $$15 \frac{9}{16}$$ inches taller than Natasha's sculpture.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you can multiply the whole number part by the denominator and add the numerator. Then, write the result as an improper fraction.

Q: How do I multiply a mixed number by a whole number?

A: To multiply a mixed number by a whole number, you can convert the mixed number to an improper fraction and then multiply.

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, you can convert them to improper fractions and then subtract.

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

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.

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

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

Common Mistakes

Mistake 1: Converting a mixed number to an improper fraction incorrectly

A: When converting a mixed number to an improper fraction, make sure to multiply the whole number part by the denominator and add the numerator.

Mistake 2: Multiplying a mixed number by a whole number incorrectly

A: When multiplying a mixed number by a whole number, make sure to convert the mixed number to an improper fraction first.

Mistake 3: Subtracting mixed numbers incorrectly

A: When subtracting mixed numbers, make sure to convert them to improper fractions first.

Tips and Tricks

Tip 1: Use a calculator to check your answers

A: If you are unsure about your calculations, use a calculator to check your answers.

Tip 2: Break down complex problems into simpler ones

A: When faced with a complex problem, break it down into simpler ones to make it easier to solve.

Tip 3: Check your units

A: Make sure to check your units when solving problems involving measurements.

Conclusion

In conclusion, the problem of comparing the heights of two sculptures, Natasha's and Maya's, is a complex one that requires careful calculations. By following the steps outlined in this article, you can solve this problem and others like it. Remember to use a calculator to check your answers, break down complex problems into simpler ones, and check your units.

Final Answer

The final answer is: $\boxed{15 \frac{9}{16}}$