Write the Fraction in Simplest Form 1/7-3(3/7n-2/7)

$\frac{1}{7} - 3 (\frac{3}{7} n - \frac{2}{7})$

Step 1

Simplify each term.

Combine $\frac{3}{7}$ and $n$ .

$\frac{1}{7} - 3 (\frac{3 n}{7} - \frac{2}{7})$

Apply the distributive property.

$\frac{1}{7} - 3 \frac{3 n}{7} - 3 (- \frac{2}{7})$

Multiply $- 3 \frac{3 n}{7}$ .

Combine $- 3$ and $\frac{3 n}{7}$ .

$\frac{1}{7} + \frac{- 3 (3 n)}{7} - 3 (- \frac{2}{7})$

Multiply $3$ by $- 3$ .

$\frac{1}{7} + \frac{- 9 n}{7} - 3 (- \frac{2}{7})$

Multiply $- 3 (- \frac{2}{7})$ .

Multiply $- 1$ by $- 3$ .

$\frac{1}{7} + \frac{- 9 n}{7} + 3 (\frac{2}{7})$

Combine $3$ and $\frac{2}{7}$ .

$\frac{1}{7} + \frac{- 9 n}{7} + \frac{3 \cdot 2}{7}$

Multiply $3$ by $2$ .

$\frac{1}{7} + \frac{- 9 n}{7} + \frac{6}{7}$

Move the negative in front of the fraction.

$\frac{1}{7} - \frac{9 n}{7} + \frac{6}{7}$

Step 2

Combine the numerators over the common denominator.

$\frac{1 - 9 n + 6}{7}$

Step 3

Add $1$ and $6$ .

$\frac{- 9 n + 7}{7}$

Step 4

Factor $- 1$ out of $- 9 n$ .

$\frac{- (9 n) + 7}{7}$

Step 5

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{- (9 n) - 1 (- 7)}{7}$

Step 6

Factor $- 1$ out of $- (9 n) - 1 (- 7)$ .

$\frac{- (9 n - 7)}{7}$

Step 7

Rewrite $- (9 n - 7)$ as $- 1 (9 n - 7)$ .

$\frac{- 1 (9 n - 7)}{7}$

Step 8

Move the negative in front of the fraction.

$- \frac{9 n - 7}{7}$