Substitute the value of the variable

Oct 13, 2025 by talynt.org 18 views

Task Overview

In this task, we will be solving a complex mathematical expression that involves multiple operations, including addition, subtraction, multiplication, and division. The expression consists of two parts: the first part requires us to calculate the result of a simple arithmetic expression, while the second part involves evaluating an expression that contains variables and fractions.

Part 1: Calculating the Result of a Simple Arithmetic Expression

The first part of the expression is: $${85 + 760 - 78}$$

To solve this expression, we need to follow the order of operations (PEMDAS):

Add 85 and 760: $85 + 760 = 845$
Subtract 78 from the result: $845 - 78 = 767$

Therefore, the result of the expression is: $\boxed{767}$

Part 2: Evaluating an Expression with Variables and Fractions

The second part of the expression is: $${185 \times z + \frac{85}{4} + 85 \times 30}$$

To evaluate this expression, we need to follow the order of operations (PEMDAS):

Multiply 185 and z: $185 \times z = 185z$
Divide 85 by 4: $\frac{85}{4} = 21.25$
Multiply 85 and 30: $85 \times 30 = 2550$
Add the results of steps 1, 2, and 3: $185z + 21.25 + 2550$

Therefore, the expression can be simplified to: $\boxed{185z + 2571.25}$

Conclusion

In this task, we have solved a complex mathematical expression that involves multiple operations, including addition, subtraction, multiplication, and division. We have broken down the expression into two parts and solved each part separately, following the order of operations (PEMDAS). The final result of the expression is: $\boxed{185z + 2571.25}$

Task Requirements

To complete this task, you need to:

Follow the order of operations (PEMDAS)
Simplify the expression by combining like terms
Evaluate the expression using the given values

Assumptions

The variable z is a numerical value
The expression is evaluated using the given values

Note

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression. PEMDAS stands for:

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

Q: How do I simplify a complex expression?

A: To simplify a complex expression, follow these steps:

Combine like terms: Combine any terms that have the same variable and coefficient.
Simplify fractions: Simplify any fractions in the expression by dividing the numerator and denominator by their greatest common divisor.
Simplify exponents: Simplify any exponential expressions by combining like terms.
Simplify parentheses: Simplify any expressions inside parentheses by following the order of operations.

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

A: A variable is a symbol that represents a value that can change. In the expression $185z + 2571.25$ , the variable is $z$ . A constant is a value that does not change. In the expression $185z + 2571.25$ , the constants are $185$ and $2571.25$ .

Q: How do I evaluate an expression with variables and fractions?

A: To evaluate an expression with variables and fractions, follow these steps:

Substitute the value of the variable: Substitute the value of the variable into the expression.
Simplify the expression: Simplify the expression by combining like terms and simplifying fractions.
Evaluate the expression: Evaluate the expression by performing any remaining operations.

Q: What is the final result of the expression $185z + 2571.25$ ?

A: The final result of the expression $185z + 2571.25$ is $\boxed{185z + 2571.25}$ . This expression cannot be simplified further because it contains a variable ( $z$ ) and a constant ( $2571.25$ ).

Q: How do I know when to use parentheses in an expression?

A: You should use parentheses in an expression when:

You need to group terms: Use parentheses to group terms that need to be evaluated together.
You need to clarify the order of operations: Use parentheses to clarify the order of operations in an expression.
You need to simplify an expression: Use parentheses to simplify an expression by grouping like terms.

Q: What is the importance of following the order of operations (PEMDAS)?

A: Following the order of operations (PEMDAS) is important because it ensures that mathematical expressions are evaluated consistently and accurately. If you do not follow the order of operations, you may get incorrect results or even change the meaning of the expression.