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Chapter 5: Problem 61

Evaluate each expression for \(x=3.6, y=5,\) and \(z=0.21\). $$ y-x+z $$

Short Answer

Expert verified
The evaluated expression is 1.61.

Step by step solution

01

Substitute the Values

Begin by substituting the given values into the expression. We have \( y = 5 \), \( x = 3.6 \), and \( z = 0.21 \). The expression is:\y - x + z = 5 - 3.6 + 0.21
02

Perform the Subtraction

Next, perform the subtraction for the terms \( 5 - 3.6 \):\5 - 3.6 = 1.4
03

Perform the Addition

Finally, add the result from the previous step to \( z \): \1.4 + 0.21 = 1.61
04

Final Result

After evaluating the expression, the result is 1.61.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Substitution
Substitution in mathematics is quite like replacing ingredients in a recipe. You take the variables in your algebraic expression and replace them with the given numerical values. For this particular exercise, you need to substitute the values of the variables as specified:
  • Assign 5 to \( y \)
  • Assign 3.6 to \( x \)
  • Assign 0.21 to \( z \)
The expression \( y - x + z \) becomes \( 5 - 3.6 + 0.21 \). Having replaced all the variables, you're now ready to simplify the expression using arithmetic operations. Remember, substitution is essential as it brings you one step closer to the numerical value of the expression.
Mastering Arithmetic Operations
Arithmetic operations form the backbone of basic mathematics and are crucial for simplifying expressions. The primary operations include addition, subtraction, multiplication, and division. When evaluating the expression \( 5 - 3.6 + 0.21 \), we use two of these operations: subtraction and addition, namely:
  • Begin by subtracting 3.6 from 5. This yields 1.4.
  • Then add 0.21 to 1.4 to complete the evaluation.
Understanding how to correctly apply these operations ensures you arrive at the correct solution. It's like following a step-by-step process to solve a puzzle, each piece represented by an operation leading you to the final answer.
Grasping the Order of Operations
The order of operations is a set of rules that determine which mathematical operations to perform first in an expression with multiple operations. This order is crucial to obtaining the correct result.
  • In this problem, we do not have parentheses or exponents, so we follow straightforward rules beginning with subtraction and finishing with addition.
  • For expressions that include several types of operations, the common helper acronym PEMDAS reminds us to solve in the order of: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Implementing this order avoids errors in calculations, ensuring each operation is conducted at the appropriate step in the evaluation.

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Most popular questions from this chapter

Choose the best estimate. \(78.6 \div 97\) a. 7.86 b. 0.786 c. 786 d. 7860

Recall from Section 1.6 that the average of a list of numbers is their total divided by how many numbers there are in the list. Use this procedure to find the average of the test scores listed in Exercises 107 and \(108 .\) If necessary, round to the nearest tenth. 86,78,91,87

Divide. Round the quotients as indicated. Divide: \(0.549 \div 0.023 .\) Round the quotient to the nearest hundredth.

Perform the indicated operation. $$ \begin{array}{r} 1000 \\ -\quad 95.71 \\ \hline \end{array} $$

Choose the best estimate. \(1.437+20.69\) a. 34 b. 22 c. 3.4 d. 2.2
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