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Chapter 2: Problem 46

Evaluate each expression. \(9 s,\) if \(s=-11\)

Short Answer

Expert verified
The expression evaluates to \(-99\).

Step by step solution

01

Substitute the Given Value

First, identify the value of the variable provided in the expression and substitute it into the expression. We have the expression \(9s\) and the variable \(s\) is given as \(-11\). Substitute \(-11\) into the expression, replacing \(s\) with \(-11\). This gives us the new expression: \(9 \times (-11)\).
02

Multiply the Numbers

Now, perform the multiplication to evaluate the expression. Multiply \(9\) by \(-11\). Remember that the product of a positive number and a negative number is negative. Hence, \(9 \times (-11) = -99\).

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Key Concepts

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

Evaluating Expressions
Evaluating expressions is a core concept in pre-algebra. An expression in mathematics is a combination of numbers, variables, and operation symbols. Evaluating simply means finding the value of an expression by performing operations based on the values given for the variables.

When you evaluate an expression, you must follow these steps:
  • Identify the variables and their given values.
  • Substitute these values in place of the variables in the expression.
  • Perform the arithmetic operations to simplify the expression into a single value.
The exercise provides an expression, such as \(9s\), and a value for \(s\), which is \(-11\). By evaluating this expression, we find exactly what it equals when \(s = -11\). Using steps like these helps build foundational skills in working with algebraic expressions.
Substitution Method
The substitution method is a handy mathematical technique used to evaluate expressions by replacing variables with their corresponding values. This process makes it easier to perform operations and solve the given problems.

Here's what you do in the substitution method:
  • First, find the variable in the expression.
  • Identify the value given for this variable.
  • Substitute the identified value directly into the expression.
For instance, in the expression \(9s\) where \(s = -11\), we substitute \(-11\) for \(s\), transforming it into \(9 \times (-11)\).
This simplifies the task to a straightforward multiplication, paving the way for getting the final value of the expression.

This method not only applies to numbers but is also valuable when dealing with equations, helping to validate solutions effectively.
Multiplication of Integers
Multiplying integers is a crucial operation in math, particularly in expressions involving positive and negative numbers. An integer is simply a whole number that can be positive, negative, or zero.

When multiplying integers, remember these rules:
  • A positive number multiplied by a positive number gives a positive result.
  • A negative number multiplied by a negative number also gives a positive result.
  • However, a positive number multiplied by a negative number, or vice versa, results in a negative number.
In the expression \(9 \times (-11)\), you multiply a positive \(9\) by a negative \(-11\), which results in \(-99\). This step is crucial for accurate evaluation, as overlooking these rules can lead to incorrect answers. Understanding these basic integer rules helps solve many pre-algebra problems confidently.

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Most popular questions from this chapter

The melting point of metal mercury is \(-39^{\circ} \mathrm{C}\). The freezing point of alcohol is \(-114^{\circ} \mathrm{C} .\) How much warmer is the melting point of mercury than the freezing point of alcohol? \(\mathbf{A}-153^{\circ} \mathrm{C}\) c \(75^{\circ} \mathrm{C}\) \(B-75^{\circ} \mathrm{C}\) D \(153^{\circ} \mathrm{C}\)

How many units apart are \(-4\) and 3 on a number line?

Evaluate each expression \(|7|\)

Name the property shown by each statement. $$9(8)(0)=0$$

Give an example of three integers whose product is negative.
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