Solve for f 3(2 1/4+f)=12 3/4

$3 (2 \frac{1}{4} + f) = 12 \frac{3}{4}$

Simplify the left side.

Simplify $3 (2 \frac{1}{4} + f)$ .

Convert $2 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$3 (2 + \frac{1}{4} + f) = 12 \frac{3}{4}$

Add $2$ and $\frac{1}{4}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$3 (2 \cdot \frac{4}{4} + \frac{1}{4} + f) = 12 \frac{3}{4}$

Combine $2$ and $\frac{4}{4}$ .

$3 (\frac{2 \cdot 4}{4} + \frac{1}{4} + f) = 12 \frac{3}{4}$

Combine the numerators over the common denominator.

$3 (\frac{2 \cdot 4 + 1}{4} + f) = 12 \frac{3}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$3 (\frac{8 + 1}{4} + f) = 12 \frac{3}{4}$

Add $8$ and $1$ .

$3 (\frac{9}{4} + f) = 12 \frac{3}{4}$

Apply the distributive property.

$3 (\frac{9}{4}) + 3 f = 12 \frac{3}{4}$

Multiply $3 (\frac{9}{4})$ .

Combine $3$ and $\frac{9}{4}$ .

$\frac{3 \cdot 9}{4} + 3 f = 12 \frac{3}{4}$

Multiply $3$ by $9$ .

$\frac{27}{4} + 3 f = 12 \frac{3}{4}$

Simplify the right side.

Convert $12 \frac{3}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{27}{4} + 3 f = 12 + \frac{3}{4}$

Add $12$ and $\frac{3}{4}$ .

To write $12$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{27}{4} + 3 f = 12 \cdot \frac{4}{4} + \frac{3}{4}$

Combine $12$ and $\frac{4}{4}$ .

$\frac{27}{4} + 3 f = \frac{12 \cdot 4}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{27}{4} + 3 f = \frac{12 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply $12$ by $4$ .

$\frac{27}{4} + 3 f = \frac{48 + 3}{4}$

Add $48$ and $3$ .

$\frac{27}{4} + 3 f = \frac{51}{4}$

Move all terms not containing $f$ to the right side of the equation.

Subtract $\frac{27}{4}$ from both sides of the equation.

$3 f = \frac{51}{4} - \frac{27}{4}$

Combine the numerators over the common denominator.

$3 f = \frac{51 - 27}{4}$

Subtract $27$ from $51$ .

$3 f = \frac{24}{4}$

Divide $24$ by $4$ .

$3 f = 6$

Divide each term in $3 f = 6$ by $3$ and simplify.

Divide each term in $3 f = 6$ by $3$ .

$\frac{3 f}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 f}{3} = \frac{6}{3}$

Divide $f$ by $1$ .

$f = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$f = 2$

Solve for f 3(2 1/4+f)=12 3/4

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