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Chapter 5: Problem 57

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

Short Answer

Expert verified
The evaluated expression is 3.81.

Step by step solution

01

Identify the Variables

We are given the problem to evaluate the expression \(x+z\) for specific values of \(x\), \(y\), and \(z\). The values given are \(x=3.6\), \(y=5\), and \(z=0.21\). In this case, \(y\) is not used, so we can focus on \(x\) and \(z\).
02

Substitute the Values

Substitute the given values of \(x\) and \(z\) into the expression. The expression is \(x+z\), so we substitute \(x=3.6\) and \(z=0.21\) to get \(3.6 + 0.21\).
03

Perform the Addition

Calculate the sum of \(3.6\) and \(0.21\). To do this, add the decimal numbers: \[ 3.6 + 0.21 = 3.81 \] This is the evaluated value of the expression.

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Key Concepts

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

Evaluating Expressions
When evaluating expressions, the first step is to comprehend what the expression represents and what values are to be used. In algebra, "evaluating" means finding the numerical value of an expression by substituting variables with their given values. In this exercise, the expression given is \(x + z\). It is important to note which variables are necessary; here, only \(x\) and \(z\) are needed.

The key to successfully evaluating the expression \(x + z\) is replacing each variable with the value provided. For this problem:
  • Identify the needed variables from the expression.
  • Substitute the values: \(x = 3.6\) and \(z = 0.21\).
  • Perform the calculation to find the solution.
Evaluating expressions becomes straightforward once you break down the steps and focus on substituting correctly with the given values.
Decimal Addition
Adding decimals may seem daunting at first, but with a simple method, it becomes very manageable. The goal is to line up the decimal points so that each digit is in its correct place, and then proceed with the standard addition.

To add \(3.6\) and \(0.21\), ensure you align the numbers by their decimal points:
  • 3.6 becomes 3.60 (adding a trailing zero for alignment).
  • 0.21 stays as is.
Once aligned:
  • Add the hundredths place: 0 + 1 = 1.
  • Add the tenths place: 6 + 2 = 8.
  • Carry over to add the ones place: 3 + 0 = 3.
The sum is therefore \(3.81\), aligning all the digits by place value ensures an accurate addition.
Variables in Algebra
Understanding variables is a fundamental aspect of algebra. Variables are symbols, often letters, that represent unknown or changeable values. In the given exercise, the letters \(x\) and \(z\) are variables.

Each variable can stand for any number, but in practice, they are often given specific values to simplify an expression or solve an equation. Here, \(x = 3.6\) and \(z = 0.21\) are the specific values provided.
  • Use variables to generalize mathematical expressions.
  • Substitute variables with known values to calculate numerical answers.
  • In algebra, operations can be simplified or solved by changing or understanding variables.
In this assignment, we see how variables are replaced with values to yield a concrete result while solving the expression \(x + z\). Knowing how to handle variables is crucial for working through more complex algebraic expressions and equations in the future.

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