Calculate The Following Expression:$\frac{8}{6} \times 45$

Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields, including science, engineering, economics, and finance. Mathematical expressions are used to represent complex problems and solutions. In this article, we will focus on simplifying a complex mathematical expression, specifically the expression $\frac{8}{6} \times 45$.

Understanding the Expression

The given expression is $\frac{8}{6} \times 45$. To simplify this expression, we need to understand the order of operations. The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Expression

Now that we have understood the expression, let's simplify it step by step.

Step 1: Simplify the Fraction

The first step is to simplify the fraction $\frac{8}{6}$. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 8 and 6 is 2.

import math

numerator = 8
denominator = 6

gcd = math.gcd(numerator, denominator)

simplified_numerator = numerator // gcd
simplified_denominator = denominator // gcd

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

The simplified fraction is $\frac{4}{3}$.

Step 2: Multiply the Simplified Fraction by 45

Now that we have simplified the fraction, let's multiply it by 45.

simplified_fraction = 4/3
multiplier = 45

result = simplified_fraction * multiplier

print(f"The result of multiplying the simplified fraction by 45 is {result}")

The result of multiplying the simplified fraction by 45 is 60.

Conclusion

In this article, we simplified a complex mathematical expression $\frac{8}{6} \times 45$ using the order of operations. We first simplified the fraction $\frac{8}{6}$ by dividing both the numerator and the denominator by their greatest common divisor (GCD). Then, we multiplied the simplified fraction by 45 to get the final result. The final result is 60.

Real-World Applications

Simplifying complex mathematical expressions is an essential skill in various fields, including science, engineering, economics, and finance. It is used to represent complex problems and solutions. For example, in finance, simplifying complex mathematical expressions is used to calculate interest rates, investment returns, and risk management.

Tips and Tricks

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

• Use the order of operations to evaluate expressions.
• Simplify fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD).
• Use multiplication and division to simplify expressions.
• Use addition and subtraction to simplify expressions.

Common Mistakes

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

• Not following the order of operations.
• Not simplifying fractions.
• Not using multiplication and division to simplify expressions.
• Not using addition and subtraction to simplify expressions.

Conclusion

$$$$

Introduction

Simplifying complex mathematical expressions is an essential skill in various fields, including science, engineering, economics, and finance. In our previous article, we simplified a complex mathematical expression $\frac{8}{6} \times 45$ using the order of operations. In this article, we will answer some frequently asked questions related to simplifying complex mathematical expressions.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify a fraction?

A: To simplify a fraction, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.

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

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 8 and 6 is 2.

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

A: To multiply a fraction by a whole number, we need to multiply the numerator of the fraction by the whole number and keep the denominator the same.

Q: What is the result of multiplying a fraction by a whole number?

A: The result of multiplying a fraction by a whole number is a new fraction with the numerator being the product of the original numerator and the whole number, and the denominator remaining the same.

Q: Can I simplify a complex mathematical expression using a calculator?

A: Yes, you can simplify a complex mathematical expression using a calculator. However, it is essential to understand the order of operations and how to simplify fractions before using a calculator.

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

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

• Not following the order of operations.
• Not simplifying fractions.
• Not using multiplication and division to simplify expressions.
• Not using addition and subtraction to simplify expressions.

Q: How do I check my work when simplifying complex mathematical expressions?

A: To check your work when simplifying complex mathematical expressions, you can:

• Use a calculator to verify your answer.
• Simplify the expression step by step.
• Check your work by plugging in the original expression and simplifying it again.

Conclusion

Simplifying complex mathematical expressions is an essential skill in various fields. In this article, we answered some frequently asked questions related to simplifying complex mathematical expressions. We covered topics such as the order of operations, simplifying fractions, multiplying fractions by whole numbers, and common mistakes to avoid. By following these tips and understanding the order of operations, you can simplify complex mathematical expressions with ease.

Real-World Applications

Simplifying complex mathematical expressions is used in various fields, including science, engineering, economics, and finance. It is used to represent complex problems and solutions. For example, in finance, simplifying complex mathematical expressions is used to calculate interest rates, investment returns, and risk management.

Tips and Tricks

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

• Use the order of operations to evaluate expressions.
• Simplify fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD).
• Use multiplication and division to simplify expressions.
• Use addition and subtraction to simplify expressions.
• Check your work by plugging in the original expression and simplifying it again.

Common Mistakes

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

• Not following the order of operations.
• Not simplifying fractions.
• Not using multiplication and division to simplify expressions.
• Not using addition and subtraction to simplify expressions.

Conclusion

Simplifying complex mathematical expressions is an essential skill in various fields. By following the tips and tricks outlined in this article, you can simplify complex mathematical expressions with ease. Remember to use the order of operations, simplify fractions, and check your work to ensure accuracy.