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Simplify the expression using the order of operations.

(18−2)+(√16))/6−2^2

3 answers

Let's simplify the expression step by step:

The expression is: \((18 - 2) + \left( \sqrt{16} \right) / 6 - 2^2\)

  1. Evaluate the parentheses and square root: \[ 18 - 2 = 16 \] \[ \sqrt{16} = 4 \]

    Now, we rewrite the expression with these values substituted: \[ (16) + \left( 4 \right) / 6 - 2^2 \]

  2. Evaluate the exponent: \[ 2^2 = 4 \]

    Now, we rewrite the expression again: \[ (16) + \left( 4 \right) / 6 - 4 \]

  3. Perform the division: \[ 4 / 6 = \frac{2}{3} \] (This can also be left as a decimal, approximately \(0.6667\), but we will keep it as a fraction.)

    Now, the expression becomes: \[ 16 + \frac{2}{3} - 4 \]

  4. Combine like terms: First, we can simplify \(16 - 4\): \[ 16 - 4 = 12 \]

    Now we have: \[ 12 + \frac{2}{3} \]

  5. Combine \(12\) and \(\frac{2}{3}\): To add \(12\) and \(\frac{2}{3}\), we convert \(12\) to a fraction with the same denominator: \[ 12 = \frac{36}{3} \]

    Now, add the two fractions: \[ \frac{36}{3} + \frac{2}{3} = \frac{36 + 2}{3} = \frac{38}{3} \]

Thus, the simplified expression is \(\frac{38}{3}\), or as a mixed number, \(12\frac{2}{3}\).

nope , try againzies

Let's simplify the expression step by step again carefully. The original equation is:

\[ \frac{(18 - 2) + \sqrt{16}}{6} - 2^2 \]

Step 1: Calculate Within the Parentheses

First, calculate \(18 - 2\):

\[ 18 - 2 = 16 \]

Next, calculate \(\sqrt{16}\):

\[ \sqrt{16} = 4 \]

Step 2: Substitute Back into the Expression

Now, substitute these values back into the expression:

\[ \frac{16 + 4}{6} - 2^2 \]

Step 3: Calculate the Addition in the Numerator

Now calculate the addition in the numerator:

\[ 16 + 4 = 20 \]

So now we have:

\[ \frac{20}{6} - 2^2 \]

Step 4: Simplify the Fraction

Next, simplify \(\frac{20}{6}\):

\[ \frac{20}{6} = \frac{10}{3} \]

Step 5: Calculate the Exponent

Now calculate \(2^2\):

\[ 2^2 = 4 \]

Step 6: Substitute and Combine

Now substitute back into the expression:

\[ \frac{10}{3} - 4 \]

To subtract \(4\) from \(\frac{10}{3}\), convert \(4\) to a fraction with the same denominator:

\[ 4 = \frac{12}{3} \]

Now we can perform the subtraction:

\[ \frac{10}{3} - \frac{12}{3} = \frac{10 - 12}{3} = \frac{-2}{3} \]

Final Answer

Thus, the simplified expression is:

\[ \frac{-2}{3} \]

Thank you for your patience, and I'm glad to help with any further questions!