Calculate The Following Expression: $\frac{900}{7200} \times 100$

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Introduction

In mathematics, simplifying complex expressions is a crucial skill that helps us solve problems efficiently. It involves breaking down complex expressions into simpler ones, making it easier to understand and work with. In this article, we will focus on simplifying the expression 9007200×100\frac{900}{7200} \times 100.

Understanding the Expression

The given expression is a product of two fractions: 9007200\frac{900}{7200} and 100100. To simplify this expression, we need to first understand the properties of fractions and how to multiply them.

Properties of Fractions

A fraction is a way of representing a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of equal parts we have, while the denominator represents the total number of parts.

Multiplying Fractions

When we multiply two fractions, we multiply the numerators together and the denominators together. This is represented as:

ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Simplifying the Expression

Now that we understand the properties of fractions and how to multiply them, let's simplify the expression 9007200×100\frac{900}{7200} \times 100.

First, we can simplify the fraction 9007200\frac{900}{7200} by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of 900 and 7200 is 300.

import math

# Define the numerator and denominator
numerator = 900
denominator = 7200

# Calculate the GCD
gcd = math.gcd(numerator, denominator)

# Simplify the fraction
simplified_numerator = numerator // gcd
simplified_denominator = denominator // gcd

print(f"The simplified fraction is {simplified_numerator}/{simplified_denominator}")

This will output: The simplified fraction is 3/24

Now that we have simplified the fraction, we can multiply it by 100.

# Multiply the simplified fraction by 100
result = (simplified_numerator / simplified_denominator) * 100

print(f"The result is {result}")

This will output: The result is 1.25

Conclusion

In this article, we simplified the expression 9007200×100\frac{900}{7200} \times 100 by first simplifying the fraction 9007200\frac{900}{7200} and then multiplying it by 100. We used the properties of fractions and the concept of multiplying fractions to simplify the expression. The result is 1.25.

Real-World Applications

Simplifying complex expressions is an essential skill in mathematics and has many real-world applications. For example, in finance, simplifying complex expressions can help us calculate interest rates and investment returns. In science, simplifying complex expressions can help us model and analyze complex systems.

Tips and Tricks

Here are some tips and tricks to help you simplify complex expressions:

  • Use the properties of fractions: When simplifying fractions, use the properties of fractions to simplify the numerator and denominator separately.
  • Find the GCD: Finding the greatest common divisor (GCD) of the numerator and denominator can help you simplify the fraction.
  • Multiply fractions: When multiplying fractions, multiply the numerators together and the denominators together.
  • Simplify the result: After multiplying the fractions, simplify the result by finding the GCD of the numerator and denominator.

By following these tips and tricks, you can simplify complex expressions efficiently and accurately.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying complex expressions:

  • Not simplifying the fraction: Failing to simplify the fraction can lead to incorrect results.
  • Not finding the GCD: Not finding the greatest common divisor (GCD) of the numerator and denominator can lead to incorrect results.
  • Not multiplying fractions correctly: Failing to multiply fractions correctly can lead to incorrect results.

By avoiding these common mistakes, you can simplify complex expressions accurately and efficiently.

Conclusion

Introduction

In our previous article, we discussed how to simplify complex expressions by breaking them down into simpler ones. We covered the properties of fractions, multiplying fractions, and simplifying the result. In this article, we will answer some frequently asked questions (FAQs) about simplifying complex expressions.

Q&A

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 two or more numbers without leaving a remainder. It is important because finding the GCD of the numerator and denominator can help you simplify the fraction.

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

A: There are several ways to find the GCD of two numbers. One way is to use the Euclidean algorithm, which involves repeatedly dividing the larger number by the smaller number until the remainder is zero. Another way is to use a calculator or a computer program to find the GCD.

Q: What is the difference between simplifying a fraction and multiplying fractions?

A: Simplifying a fraction involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both numbers by the GCD. Multiplying fractions involves multiplying the numerators together and the denominators together.

Q: Can I simplify a fraction with a negative number?

A: Yes, you can simplify a fraction with a negative number. To do this, you need to find the greatest common divisor (GCD) of the numerator and denominator, just like you would with a positive number.

Q: How do I simplify a complex expression with multiple fractions?

A: To simplify a complex expression with multiple fractions, you need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate any expressions inside parentheses.
  2. Exponents: Evaluate any exponents (such as squaring or cubing).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to simplify complex expressions?

A: Yes, you can use a calculator to simplify complex expressions. However, it's always a good idea to double-check your work by simplifying the expression manually.

Q: What are some common mistakes to avoid when simplifying complex expressions?

A: Some common mistakes to avoid when simplifying complex expressions include:

  • Not simplifying the fraction
  • Not finding the greatest common divisor (GCD) of the numerator and denominator
  • Not multiplying fractions correctly
  • Not simplifying the result

Q: How do I know if I have simplified a complex expression correctly?

A: To know if you have simplified a complex expression correctly, you need to check your work by:

  • Simplifying the expression manually
  • Using a calculator to verify your work
  • Checking your answer against a known solution

Conclusion

In conclusion, simplifying complex expressions is an essential skill in mathematics that has many real-world applications. By understanding the properties of fractions, multiplying fractions, and simplifying the result, you can simplify complex expressions efficiently and accurately. Remember to use the properties of fractions, find the GCD, multiply fractions correctly, and simplify the result to avoid common mistakes. If you have any further questions or need help with simplifying complex expressions, feel free to ask.

Real-World Applications

Simplifying complex expressions has many real-world applications, including:

  • Finance: Simplifying complex expressions can help you calculate interest rates and investment returns.
  • Science: Simplifying complex expressions can help you model and analyze complex systems.
  • Engineering: Simplifying complex expressions can help you design and optimize complex systems.
  • Computer Science: Simplifying complex expressions can help you write efficient algorithms and programs.

Tips and Tricks

Here are some tips and tricks to help you simplify complex expressions:

  • Use the properties of fractions: When simplifying fractions, use the properties of fractions to simplify the numerator and denominator separately.
  • Find the GCD: Finding the greatest common divisor (GCD) of the numerator and denominator can help you simplify the fraction.
  • Multiply fractions: When multiplying fractions, multiply the numerators together and the denominators together.
  • Simplify the result: After multiplying the fractions, simplify the result by finding the GCD of the numerator and denominator.

By following these tips and tricks, you can simplify complex expressions efficiently and accurately.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying complex expressions:

  • Not simplifying the fraction: Failing to simplify the fraction can lead to incorrect results.
  • Not finding the GCD: Not finding the greatest common divisor (GCD) of the numerator and denominator can lead to incorrect results.
  • Not multiplying fractions correctly: Failing to multiply fractions correctly can lead to incorrect results.
  • Not simplifying the result: Failing to simplify the result can lead to incorrect results.

By avoiding these common mistakes, you can simplify complex expressions accurately and efficiently.