Multiply the Fraction by 8

Oct 13, 2025 by magicalceylontours.com 87 views

Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by applying the order of operations (PEMDAS/BODMAS). This concept is crucial in various mathematical operations, including algebra, geometry, and calculus. In this article, we will evaluate the expression $8^2 + \left( \frac{9}{3} \cdot 8 \right)$ and provide a step-by-step solution to simplify the expression.

Understanding the Expression

The given expression is $8^2 + \left( \frac{9}{3} \cdot 8 \right)$ . To evaluate this expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Evaluating the Expression

To evaluate the expression, we will follow the order of operations:

Evaluate the Exponent: The first step is to evaluate the exponent $8^2$ . This means multiplying 8 by itself, which gives us $8^2 = 64$ .
Evaluate the Fraction: The next step is to evaluate the fraction $\frac{9}{3}$ . This means dividing 9 by 3, which gives us $\frac{9}{3} = 3$ .
Multiply the Fraction by 8: Now that we have the value of the fraction, we can multiply it by 8. This gives us $3 \cdot 8 = 24$ .
Add the Results: Finally, we can add the results of the exponent and the multiplication. This gives us $64 + 24 = 88$ .

Conclusion

In conclusion, the value of the expression $8^2 + \left( \frac{9}{3} \cdot 8 \right)$ is 88. This is obtained by following the order of operations and simplifying the expression step by step.

Step-by-Step Solution

Here is the step-by-step solution to evaluate the expression:

Evaluate the exponent: $8^2 = 64$
Evaluate the fraction: $\frac{9}{3} = 3$
Multiply the fraction by 8: $3 \cdot 8 = 24$
Add the results: $64 + 24 = 88$

Real-World Applications

Evaluating expressions is a crucial concept in various real-world applications, including:

Science: In science, evaluating expressions is used to model real-world phenomena, such as the motion of objects, the growth of populations, and the behavior of physical systems.
Engineering: In engineering, evaluating expressions is used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Finance: In finance, evaluating expressions is used to calculate interest rates, investment returns, and other financial metrics.

Tips and Tricks

Here are some tips and tricks to help you evaluate expressions:

Follow the Order of Operations: Always follow the order of operations (PEMDAS/BODMAS) when evaluating expressions.
Use Parentheses: Use parentheses to group numbers and operations, making it easier to evaluate the expression.
Simplify the Expression: Simplify the expression by combining like terms and eliminating unnecessary operations.

Common Mistakes

Here are some common mistakes to avoid when evaluating expressions:

Not Following the Order of Operations: Failing to follow the order of operations can lead to incorrect results.
Not Using Parentheses: Failing to use parentheses can lead to confusion and incorrect results.
Not Simplifying the Expression: Failing to simplify the expression can lead to unnecessary complexity and incorrect results.

Conclusion

In conclusion, evaluating expressions is a fundamental concept in mathematics that involves simplifying mathematical expressions by applying the order of operations (PEMDAS/BODMAS). By following the order of operations and simplifying the expression, we can obtain the correct result. In this article, we evaluated the expression $8^2 + \left( \frac{9}{3} \cdot 8 \right)$ and provided a step-by-step solution to simplify the expression. We also discussed real-world applications, tips and tricks, and common mistakes to avoid when evaluating expressions.

Introduction

In our previous article, we evaluated the expression $8^2 + \left( \frac{9}{3} \cdot 8 \right)$ and provided a step-by-step solution to simplify the expression. In this article, we will answer some frequently asked questions (FAQs) related to evaluating 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:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Q: Why is it important to follow the order of operations?

A: Following the order of operations is important because it ensures that we perform the operations in the correct order, which is necessary to obtain the correct result.

Q: What is the difference between PEMDAS and BODMAS?

A: PEMDAS and BODMAS are two different notations for the order of operations. PEMDAS stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction," while BODMAS stands for "Brackets, Orders, Division, Multiplication, Addition, and Subtraction." Both notations refer to the same order of operations.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations:

Evaluate any expressions inside parentheses.
Evaluate any exponents.
Evaluate any multiplication and division operations from left to right.
Evaluate any addition and subtraction operations from left to right.

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

A: A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a fraction as a number with a point. For example, the fraction 1/2 is equal to the decimal 0.5.

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

A: To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert the fraction 1/2 to a decimal, divide 1 by 2, which gives 0.5.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change.

Q: How do I evaluate an expression with variables?

A: To evaluate an expression with variables, follow the order of operations and substitute the values of the variables into the expression.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal, while an expression is a mathematical statement that contains variables, constants, and operations.

Q: How do I solve an equation?

A: To solve an equation, follow these steps:

Simplify the equation by combining like terms.
Isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Check your solution by plugging it back into the original equation.

Conclusion

In conclusion, evaluating expressions is a fundamental concept in mathematics that involves simplifying mathematical expressions by applying the order of operations (PEMDAS/BODMAS). By following the order of operations and simplifying the expression, we can obtain the correct result. In this article, we answered some frequently asked questions (FAQs) related to evaluating expressions, including the order of operations, the difference between PEMDAS and BODMAS, and how to evaluate expressions with multiple operations.

Tips and Tricks

Here are some tips and tricks to help you evaluate expressions:

Follow the Order of Operations: Always follow the order of operations (PEMDAS/BODMAS) when evaluating expressions.
Use Parentheses: Use parentheses to group numbers and operations, making it easier to evaluate the expression.
Simplify the Expression: Simplify the expression by combining like terms and eliminating unnecessary operations.
Check Your Work: Check your work by plugging the result back into the original expression.

Common Mistakes

Here are some common mistakes to avoid when evaluating expressions:

Not Following the Order of Operations: Failing to follow the order of operations can lead to incorrect results.
Not Using Parentheses: Failing to use parentheses can lead to confusion and incorrect results.
Not Simplifying the Expression: Failing to simplify the expression can lead to unnecessary complexity and incorrect results.
Not Checking Your Work: Failing to check your work can lead to incorrect results.