Solve for f 7/12f=2 1/24

$\frac{7}{12} f = 2 \frac{1}{24}$

Simplify the left side.

Combine $\frac{7}{12}$ and $f$ .

$\frac{7 f}{12} = 2 \frac{1}{24}$

Simplify the right side.

Convert $2 \frac{1}{24}$ to an improper fraction.

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

$\frac{7 f}{12} = 2 + \frac{1}{24}$

Add $2$ and $\frac{1}{24}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$\frac{7 f}{12} = 2 \cdot \frac{24}{24} + \frac{1}{24}$

Combine $2$ and $\frac{24}{24}$ .

$\frac{7 f}{12} = \frac{2 \cdot 24}{24} + \frac{1}{24}$

Combine the numerators over the common denominator.

$\frac{7 f}{12} = \frac{2 \cdot 24 + 1}{24}$

Simplify the numerator.

Multiply $2$ by $24$ .

$\frac{7 f}{12} = \frac{48 + 1}{24}$

Add $48$ and $1$ .

$\frac{7 f}{12} = \frac{49}{24}$

Multiply both sides of the equation by $\frac{12}{7}$ .

$\frac{12}{7} \cdot \frac{7 f}{12} = \frac{12}{7} \cdot \frac{49}{24}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{7} \cdot \frac{7 f}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{7} \cdot \frac{7 f}{12} = \frac{12}{7} \cdot \frac{49}{24}$

Rewrite the expression.

$\frac{1}{7} (7 f) = \frac{12}{7} \cdot \frac{49}{24}$

Cancel the common factor of $7$ .

Factor $7$ out of $7 f$ .

$\frac{1}{7} (7 (f)) = \frac{12}{7} \cdot \frac{49}{24}$

Cancel the common factor.

$\frac{1}{7} (7 f) = \frac{12}{7} \cdot \frac{49}{24}$

Rewrite the expression.

$f = \frac{12}{7} \cdot \frac{49}{24}$

Simplify the right side.

Simplify $\frac{12}{7} \cdot \frac{49}{24}$ .

Cancel the common factor of $12$ .

Factor $12$ out of $24$ .

$f = \frac{12}{7} \cdot \frac{49}{12 (2)}$

Cancel the common factor.

$f = \frac{12}{7} \cdot \frac{49}{12 \cdot 2}$

Rewrite the expression.

$f = \frac{1}{7} \cdot \frac{49}{2}$

Cancel the common factor of $7$ .

Factor $7$ out of $49$ .

$f = \frac{1}{7} \cdot \frac{7 (7)}{2}$

Cancel the common factor.

$f = \frac{1}{7} \cdot \frac{7 \cdot 7}{2}$

Rewrite the expression.

$f = \frac{7}{2}$

The result can be shown in multiple forms.

Exact Form:

$f = \frac{7}{2}$

Decimal Form:

$f = 3.5$

Mixed Number Form:

$f = 3 \frac{1}{2}$

Solve for f 7/12f=2 1/24

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