Solve for f 1/4+7f=5/6

$\frac{1}{4} + 7 f = \frac{5}{6}$

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

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Subtract $\frac{1}{4}$ from both sides of the equation.

$7 f = \frac{5}{6} - \frac{1}{4}$

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 f = \frac{5}{6} \cdot \frac{2}{2} - \frac{1}{4}$

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$7 f = \frac{5}{6} \cdot \frac{2}{2} - \frac{1}{4} \cdot \frac{3}{3}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{5}{6}$ and $\frac{2}{2}$ .

$7 f = \frac{5 \cdot 2}{6 \cdot 2} - \frac{1}{4} \cdot \frac{3}{3}$

Multiply $6$ by $2$ .

$7 f = \frac{5 \cdot 2}{12} - \frac{1}{4} \cdot \frac{3}{3}$

Multiply $\frac{1}{4}$ and $\frac{3}{3}$ .

$7 f = \frac{5 \cdot 2}{12} - \frac{3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$7 f = \frac{5 \cdot 2}{12} - \frac{3}{12}$

Combine the numerators over the common denominator.

$7 f = \frac{5 \cdot 2 - 3}{12}$

Simplify the numerator.

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Multiply $5$ by $2$ .

$7 f = \frac{10 - 3}{12}$

Subtract $3$ from $10$ .

$7 f = \frac{7}{12}$

Divide each term by $7$ and simplify.

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Divide each term in $7 f = \frac{7}{12}$ by $7$ .

$\frac{7 f}{7} = \frac{7}{12} \cdot \frac{1}{7}$

Cancel the common factor of $7$ .

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Cancel the common factor.

$\frac{7 f}{7} = \frac{7}{12} \cdot \frac{1}{7}$

Divide $f$ by $1$ .

$f = \frac{7}{12} \cdot \frac{1}{7}$

Cancel the common factor of $7$ .

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Cancel the common factor.

$f = \frac{7}{12} \cdot \frac{1}{7}$

Rewrite the expression.

$f = \frac{1}{12}$

The result can be shown in multiple forms.

Exact Form:

$f = \frac{1}{12}$

Decimal Form:

$f = 0.08\overline{3}$

Solve for f 1/4+7f=5/6

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