Problem 27 Evaluate each expression. $$a ... [FREE SOLUTION]

Chapter 2: Problem 27

Evaluate each expression. $$a b \div 6, \text { if } a=-12 \text { and } b=-8$$

Short Answer

Expert verified

The value of the expression is 16.

Step by step solution

Substitute Variables

First, substitute the values of the variables into the expression. We have been given that $a = -12$ and $b = -8$. The expression $a b \div 6$ becomes $(-12) \times (-8) \div 6$.

Multiply the Numbers

Next, perform the multiplication operation. Multiply $-12$ by $-8$. Recall that the product of two negative numbers is positive. So, $(-12) \times (-8) = 96$.

Divide the Result

Now, divide the result from the multiplication by 6. We have $96 \div 6 = 16$. This step gives us the final value of the expression.

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Key Concepts

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

Variable Substitution

Variable substitution is the process of replacing variables in an expression with their given values. It is essential for evaluating expressions where specific numbers replace placeholders, like letters.

Identify the variables in the expression.
Find the given value for each variable.
Replace each variable in the expression with its respective numerical value.

For instance, in the expression $a b \div 6$, we substitute $a = -12$ and $b = -8$. This replacement transforms the expression into $(-12) \times (-8) \div 6$. This substitution forms the first crucial step in solving the expression.

Multiplication of Integers

When multiplying integers, especially those with signs, it's important to remember the basic sign rules. For integers:

The product of two positive numbers is positive.
The product of two negative numbers is positive.
The product of a positive and a negative number is negative.

In our example, multiplying $-12$ and $-8$, both being negative, results in a positive product. Using the rules mentioned, $(-12) \times (-8) = 96$. This multiplication step is vital as it simplifies the expression for the next operation.

Division of Numbers

Division is the process of determining how many times one number is contained within another. When dealing with division of numbers, you are essentially searching for how many times the divisor can fit into the dividend.In this exercise, after obtaining the product 96 from multiplying $-12$ and $-8$, we divide 96 by 6. This operation is straightforward as both numbers are positive, resulting from the previous multiplication process. Dividing gives us: \[ 96 \div 6 = 16 \]This final step completes the evaluation of the initial expression, providing us with a solution of 16.

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91影视

Evaluate each expression. $$a b \div 6, \text { if } a=-12 \text { and } b=-8$$

Short Answer

Step by step solution

Substitute Variables

Multiply the Numbers

Divide the Result

Key Concepts

Variable Substitution

Multiplication of Integers

Division of Numbers

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