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Chapter 2: Problem 68

Find the value of each expression for the given values. \(a b+6 b c ; a=0, b=-1,\) and \(c=9\)

Short Answer

Expert verified
The value of the expression is -54.

Step by step solution

01

Substitute the Given Values

Start by identifying the given values for the variables in the expression. You have \( a = 0 \), \( b = -1 \), and \( c = 9 \). Substitute these values into the expression \( ab + 6bc \). This becomes \( 0 \times (-1) + 6 \times (-1) \times 9 \).
02

Simplify the Expression

Calculate each part of the expression. First, \( 0 \times (-1) = 0 \). Next, calculate \( 6 \times (-1) = -6 \), and then \( -6 \times 9 = -54 \).
03

Combine the Results

Add the results from the previous calculations: \( 0 + (-54) = -54 \). Thus, the value of the expression \( ab + 6bc \) for the given values is \(-54\).

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Key Concepts

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

Expression Evaluation
Expression evaluation is the process of calculating the value of a mathematical expression. To successfully evaluate an expression, you should follow a series of logical steps that lead to a final answer.

In our exercise, we have the expression: \( ab + 6bc \). Evaluating this expression means determining its value when specific numbers replace the variables. To do this, follow these simple steps:
  • Identify the values given for each variable
  • Substitute these numbers into the expression
  • Perform the arithmetic operations to simplify the expression
Understanding this concept helps in dealing with a wide range of algebraic problems. It鈥檚 essential to approach expression evaluation with careful attention to the order of operations: first multiplying or dividing, then adding or subtracting.
Substitution Method
The substitution method involves replacing variables in an algebraic expression with their given values. This method is useful when you need to find the exact numerical value of an expression. In the given problem, we need to substitute:
  • \( a = 0 \)
  • \( b = -1 \)
  • \( c = 9 \)
Substituting is straightforward鈥攋ust replace each variable with the number given beside it. For the expression \( ab + 6bc \), it becomes \( 0 \times (-1) + 6 \times (-1) \times 9 \) after substitution.

This simple technique helps to transform a variable expression into plain arithmetic operations, making complicated expressions more manageable by converting them into calculations with known numbers.
Integer Multiplication
Integer multiplication is one of the building blocks of mathematics. It involves multiplying two or more whole numbers (integers). In algebra, it simplifies during expression evaluation when variables are replaced by integers.

In the given exercise, we perform integer multiplication with
  • \( 0 \times (-1) = 0 \)
  • \( 6 \times (-1) = -6 \)
  • \( -6 \times 9 = -54 \)
These steps show how integer multiplication works: by multiplying the numbers directly while considering the sign. Negative multiplied by negative gives a positive, while a negative by positive (or vice versa) remains negative.

By understanding integer multiplication, one can easily handle various algebraic expressions, ensuring smooth simplifications and prompt calculations.

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