Evaluate Using the Given Value p(q÷3-p) ; use p=-6 ; and q=-3

Solution:

Step 1:

Substitute the value of $p$ with $-6$ into the given expression. We get $(-6)(q÷3-(-6))$.

Step 2:

Now, replace the value of $q$ with $-3$ in the expression. This leads to $(-6)(-3÷3-(-6))$.

Step 3:

Begin simplifying the terms within the expression.

Step 3.1:

Divide $-3$ by $3$ to get $-6(-1-(-6))$.

Step 3.2:

Change the subtraction of a negative number to addition and simplify $-1$ times $-6$ to get $-6(-1+6)$.

Step 4:

Further simplify the expression.

Step 4.1:

Combine $-1$ and $6$ to obtain $-6\cdot 5$.

Step 4.2:

Finally, multiply $-6$ by $5$ to get the result $-30$.

Knowledge Notes:

The problem involves evaluating an algebraic expression using specific values for the variables $p$ and $q$. The process includes the following steps:

1. Substitution: Replace the variables with their given values. This is a direct application of the substitution property of equality, which states that if $a=b$, then $a$ can be substituted for $b$ in any expression.

2. Order of Operations: Follow the correct order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In this case, division is performed before addition and subtraction.

3. Simplifying Expressions: Combine like terms and perform arithmetic operations to simplify the expression. This involves understanding how to work with negative numbers, such as knowing that subtracting a negative is equivalent to adding a positive.

4. Multiplication of Integers: When multiplying integers, remember that the product of two numbers with the same sign is positive, while the product of two numbers with different signs is negative.

5. Final Evaluation: After simplifying, you should reach a numerical value that represents the value of the expression for the given values of $p$ and $q$.