Pre-Algebra Examples

$9 + \frac{1}{2} \cdot (7 n - 26) - 8 n$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$9 + \frac{1}{2} (7 n) + \frac{1}{2} \cdot - 26 - 8 n$

Step 1.2

Multiply $\frac{1}{2} (7 n)$ .

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Step 1.2.1

Combine $7$ and $\frac{1}{2}$ .

$9 + \frac{7}{2} n + \frac{1}{2} \cdot - 26 - 8 n$

Step 1.2.2

Combine $\frac{7}{2}$ and $n$ .

$9 + \frac{7 n}{2} + \frac{1}{2} \cdot - 26 - 8 n$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $- 26$ .

$9 + \frac{7 n}{2} + \frac{1}{2} \cdot (2 (- 13)) - 8 n$

Step 1.3.2

Cancel the common factor.

$9 + \frac{7 n}{2} + \frac{1}{2} \cdot (2 \cdot - 13) - 8 n$

Step 1.3.3

Rewrite the expression.

$9 + \frac{7 n}{2} - 13 - 8 n$

Step 2

Subtract $13$ from $9$ .

$\frac{7 n}{2} - 4 - 8 n$

Step 3

To write $- 8 n$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 n}{2} - 8 n \cdot \frac{2}{2} - 4$

Step 4

Simplify terms.

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Step 4.1

Combine $- 8 n$ and $\frac{2}{2}$ .

$\frac{7 n}{2} + \frac{- 8 n \cdot 2}{2} - 4$

Step 4.2

Combine the numerators over the common denominator.

$\frac{7 n - 8 n \cdot 2}{2} - 4$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $n$ out of $7 n - 8 n \cdot 2$ .

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Step 5.1.1.1

Factor $n$ out of $7 n$ .

$\frac{n \cdot 7 - 8 n \cdot 2}{2} - 4$

Step 5.1.1.2

Factor $n$ out of $- 8 n \cdot 2$ .

$\frac{n \cdot 7 + n (- 8 \cdot 2)}{2} - 4$

Step 5.1.1.3

Factor $n$ out of $n \cdot 7 + n (- 8 \cdot 2)$ .

$\frac{n (7 - 8 \cdot 2)}{2} - 4$

Step 5.1.2

Multiply $- 8$ by $2$ .

$\frac{n (7 - 16)}{2} - 4$

Step 5.1.3

Subtract $16$ from $7$ .

$\frac{n \cdot - 9}{2} - 4$

Step 5.2

Move $- 9$ to the left of $n$ .

$\frac{- 9 \cdot n}{2} - 4$

Step 5.3

Move the negative in front of the fraction.

$- \frac{9 n}{2} - 4$