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Chapter 5: Problem 59

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

Short Answer

Expert verified
3.39

Step by step solution

01

Substitute Given Values

Substitute the given values into the expression. For this expression, substitute 3.6 for \(x\) and 0.21 for \(z\) to get the new expression:\[3.6 - 0.21\]
02

Perform the Subtraction

Subtract 0.21 from 3.6. It can help to lay this out vertically if needed:\[\begin{array}{c} 3.60 \- 0.21 \\hline 3.39\end{array}\]The difference is 3.39.

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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 four basic arithmetic operations. It involves taking one number away from another. Think of it as finding out how much is left after something is removed. In the example problem, subtraction is used to find the difference between the numbers given for variables \(x\) and \(z\).

When subtracting numbers, remember these key steps:
  • Align the numbers by their decimal points, which ensures that each place value is correctly subtracted from its counterpart.
  • Start subtracting from the rightmost digit, which is usually the smallest place value (like hundredths or tenths).
  • If the top number is smaller than the bottom number, you may need to "borrow" from the next left digit.
In our expression, we subtracted 0.21 from 3.6, and as a result, we calculated the difference to be 3.39. This method ensures you don't accidentally place values in the wrong place, especially when dealing with decimal numbers.
Decimal Numbers
Decimal numbers are used to represent fractions in a more readable form. They have two parts: a whole number and a fractional part, separated by a decimal point. In "3.6," for instance, "3" is the whole number and "6" represents "six-tenths," occupying the first position after the decimal point.

The significance of decimal places is as follows:
  • The first digit to the right of the decimal is the tenths place.
  • The second digit to the right of the decimal is the hundredths place.
  • Further digits move into thousandths, ten-thousandths, etc.
When performing operations like subtraction, keeping your decimals aligned is crucial. If you misalign them, the numbers will represent completely different values, leading to errors in calculation. For the example \(3.6 - 0.21\), aligning the decimal points allowed for a straightforward subtraction, giving the result of 3.39.
Evaluating Expressions
Evaluating expressions is the process of finding out the value of an expression by substituting variables with given numbers. It's like checking the final price of a product after applying coupons and discounts.

Here's how to effectively evaluate expressions:
  • Identify all variables in the expression.
  • Substitute each variable with the numbers provided in the problem.
  • Follow the order of operations to simplify the expression step by step.
In the given example, only subtraction was needed to evaluate the expression \(x - z\), where \(x\) was replaced by 3.6 and \(z\) by 0.21. Simplifying, the expression led to 3.39.

This simple substitution and operation are key parts of evaluating more complex expressions. Ensuring each step is done correctly prevents errors and leads to accurate results.

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