Problem 126 - Elementary Algebra

Question

Problem: Evaluate: \(-3^{2}+8 \div(-2)\) Incorrect Answer: \(-3^{2}+8 \div(-2)\) $$ \begin{aligned} &=9+8 \div(-2) \\ &=9+(-4) \\ &=5 \end{aligned} $$

Step-by-Step Solution

Answer

The correct value of the expression is -13.

Step 1: Evaluate the exponent

First, evaluate the exponent term Given the expression 3^{2} should be evaluated first, which gives Notice the negative sign outside the exponent. Therefore, = -9

Step 2: Evaluate the division

Next, evaluate the division term in the expression Draw a clear understanding of proper precedence. Let's compute gives -4

Step 3: Combine the results

Finally, combine the results from the previous steps -9 - 4 = -13

Key Concepts

Exponents

Exponents, also known as powers, are a way to represent repeated multiplication of the same number by itself. For example, in the term \(3^2\), the number 3 is being multiplied by itself. \(3^2\) means \(3 \times 3\), which equals 9.
The important thing to remember is to apply the exponent before moving on to other operations like addition or division. Always look inside the exponent first if the base has any operations.

Division

Division is the process of splitting a number into equal parts. When you see a division symbol ('\div') in an arithmetic expression, it means you should divide the number before the symbol by the number after it. For example, \(8 \div(-2)\) can be read as \(8\) divided by \(-2\). This gives \(-4\) because dividing a positive number by a negative number results in a negative number.
Always remember to perform division only after handling any exponents in your order of operations.

Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign (-). They can be tricky in arithmetic operations because they change how addition, subtraction, multiplication, and division work.
When you add a negative number, it's like subtracting its positive counterpart. For example, \(-9\) + \(-4\) = \(-13\).
Similarly, keep in mind that multiplying or dividing two negative numbers gives a positive result, while multiplying or dividing a positive and a negative number results in a negative product or quotient.

PEMDAS

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition, and Subtraction (from left to right). It's a mnemonic to help remember the order of operations in math. Following PEMDAS ensures that arithmetic operations are performed properly to get the correct result.
In the given problem, apply PEMDAS by first solving the exponent \(-3^2\), then division \(8 \div -2\). Finally, perform the addition/subtraction, which combines the results of previous steps \(-9 - 4 = -13\).