Problem 68 - Elementary Algebra

Question

\(5-4^{2} \div 2\)

Step-by-Step Solution

Answer

-3

Step 1 - Evaluate the Exponent

First, evaluate the exponent in the expression. Calculate the value of the exponent: \( 4^{2} = 16 \). This gives us the new expression: \( 5 - 16 \div 2 \)

Step 2 - Perform Division

Next, perform the division operation in the expression. Divide 16 by 2: \[ 16 \div 2 = 8 \] This results in the new expression: \( 5 - 8 \)

Step 3 - Perform Subtraction

Finally, perform the subtraction operation in the expression: \[ 5 - 8 = -3 \] This gives us the final answer.

Key Concepts

Evaluate the Exponent

When faced with an expression like \(5 - 4^{2} \div 2\), the first step is to evaluate the exponent. Think of an exponent as a way to multiply a number by itself a specific number of times. Here, you have \(4^{2}\), which means 4 multiplied by itself. \(4 \times 4 = 16\). This simplifies our original problem to \(5 - 16 \div 2\). Always solve exponents first before moving on to other operations.

Performing Division

Next, we need to perform the division in the expression \(5 - 16 \div 2\). Division might seem tricky, but it's just about splitting something into equal parts. \Dividing 16 by 2 means figuring out how many times 2 fits into 16. The answer is 8 because \(16 \div 2 = 8\). Now our expression is simplified to \(5 - 8\).

Performing Subtraction

The final step in solving our expression \(5 - 8\) is to perform the subtraction. Subtraction means taking one number away from another. Here, you are taking 8 away from 5. Since 8 is larger than 5, you will end up with a negative number. Think of it this way: if you have 5 and owe someone 8, you're in debt by 3. So, \(5 - 8 = -3\).