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Chapter 5: Problem 60

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

Short Answer

Expert verified
The expression evaluates to 4.79.

Step by step solution

01

Identify the given values

We are given the values of the variables: \( x = 3.6 \), \( y = 5 \), and \( z = 0.21 \). These will be used to evaluate the expression.
02

Substitute the values into the expression

Take the expression \( y - z \) and substitute the values of \( y = 5 \) and \( z = 0.21 \) into it. This gives us \( 5 - 0.21 \).
03

Calculate the result

Perform the subtraction: \( 5 - 0.21 = 4.79 \).

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Key Concepts

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

Subtraction
Subtraction is one of the fundamental arithmetic operations. It involves finding the difference between numbers. Simply put, we take one number away from another. When faced with an expression such as \( y - z \), the operation is straightforward. You are reducing the value of \( y \) by \( z \).
  • In the problem provided, you subtract \(0.21\) from \(5\).
  • This process can also be visualized on a number line by moving left from the number \(5\) by \(0.21\) units.
This simplification gives us a more intuitive way of understanding subtraction. It's not merely an operation, but a method of determining how much is left or how much it changes after removing a specific amount. In arithmetic problems involving real numbers, visualization can help. Remember, subtraction is the inverse of addition.
Variable Substitution
Variable substitution is a critical skill in algebra and prealgebra. It allows us to evaluate expressions by replacing variables with their actual numerical values. In our problem, we knew \( y = 5 \) and \( z = 0.21 \).
  • First, identify what each variable represents; in this case, integers or decimals.
  • The expression \( y - z \) transforms into \( 5 - 0.21 \) once we apply substitution.
This conversion is simple but powerful. It changes abstract expressions into specific numbers you can directly solve. Practicing variable substitution helps in understanding complex algebraic expressions. Remember, accurate substitution is essential: getting one value wrong can lead to incorrect answers.
Arithmetic Operations
Arithmetic operations form the building blocks of mathematics. These include addition, subtraction, multiplication, and division. In this exercise, you primarily perform subtraction, but understanding all operations, in general, is crucial. Here is why they matter:
  • They give structure to mathematical expressions.
  • Each operation has unique properties and follows certain rules that we must adhere to.
With arithmetic, fractions, whole numbers, and decimals can all be manipulated smoothly. In this particular expression, understanding subtraction helps determine the difference between two numbers.
Adding, subtracting, multiplying, and dividing are all skills that improve your math fluency and make solving complex problems more manageable. Thus, the practice of arithmetic operations refines mental math capabilities.

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Most popular questions from this chapter

In your own words, describe how to quickly divide a number by a power of 10 such as \(10,100,1000,\) etc.

Divide. \(\frac{23.8}{0.035}\)

Perform the indicated operation. \(\frac{3}{5}-\frac{7}{10}\)

Divide. \(13.49 \div(-10,000)\)

During an experiment, the following times (in seconds) were recorded: $$ 7.8,6.9,7.5,4.7,6.9,7.0 . $$ Find the mean.
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