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Chapter 5: Problem 72

Evaluate each expression for \(x=5.65, y=-0.8,\) and \(z=4.52 .\) \(y \div 2\)

Short Answer

Expert verified
The expression evaluates to \(-0.4\).

Step by step solution

01

Substitute Values

First, identify the value of the variable given in the expression. We have the expression \(y \div 2\) where \(y = -0.8\). Substitute \(-0.8\) for \(y\).
02

Perform Division

Now, perform the division operation by dividing \(-0.8\) by \(2\). \[\text{Expression} = \frac{-0.8}{2} = -0.4\]
03

Verify Calculation

Verify your division calculation to ensure accuracy. Check that dividing a negative number by a positive number should yield a negative result. In this case, \(-0.8\) divided by \(2\) gives \(-0.4\).

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Key Concepts

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

Substituting Values in Algebraic Expressions
Substituting values is a fundamental skill in algebra. It is the process of replacing variables in an expression with given numbers. This allows us to evaluate the expression to find its numerical value.

Let's take the example of the expression: \(y \div 2\). In the problem, the value of \(y\) is provided as \(-0.8\). To substitute, you simply replace \(y\) with \(-0.8\). This results in the expression changing to \(-0.8 \div 2\).

Key points for successful substitutions:
  • Ensure that the given value directly corresponds to the variable present in the expression.
  • Be mindful of the sign of the number (positive or negative) when substituting.
  • Write down the substituted expression carefully to avoid any errors in calculation.
Substitution helps transform complex algebraic expressions into simpler numerical calculations.
Working with Negative Numbers
Handling negative numbers can sometimes be tricky, especially when performing operations like division. Negative numbers are numbers less than zero and are typically represented with a minus sign.

In mathematical operations, remember:
  • A negative number multiplied or divided by a positive number results in a negative number.
  • A negative divided by a negative gives a positive result.
  • Consistently checking the signs during operations helps prevent mistakes.
In our example, dividing \(-0.8\) by 2:
  • The numerator is negative, and the denominator is positive.
  • The result will be a negative value, \(-0.4\).
Always remember that the sign of the outcome depends largely on the combination of signs of the numbers involved.
Understanding Division in Arithmetic Operations
Division is one of the basic arithmetic operations, involving splitting a number into defined parts. Conceptually, it can be thought of as determining how many times one number is contained within another.

When performing division, especially with fractions and decimals like \(-0.8\), follow these steps:
  • Ensure the division is set up correctly with the correct numerator (the number being divided) and denominator (the number by which you divide).
  • Apply signs correctly based on whether the numbers are positive or negative; a negative divided by a positive yields a negative.
  • Perform the division, which involves dividing the absolute values and then applying the sign determined by the rules of division.
For \(-0.8 \div 2\), you divide the absolute values: \(0.8 \div 2 = 0.4\). Since the rules say a negative number divided by a positive number results in a negative, the final result is \(-0.4\).

These arithmetic operations are crucial for solving algebraic expressions efficiently and accurately.

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Most popular questions from this chapter

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