Solve for h 3/4h-12=8 5/8

$\frac{3}{4} h - 12 = 8 \frac{5}{8}$

Simplify the left side.

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

$\frac{3 h}{4} - 12 = 8 \frac{5}{8}$

Simplify the right side.

Convert $8 \frac{5}{8}$ to an improper fraction.

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

$\frac{3 h}{4} - 12 = 8 + \frac{5}{8}$

Add $8$ and $\frac{5}{8}$ .

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

$\frac{3 h}{4} - 12 = 8 \cdot \frac{8}{8} + \frac{5}{8}$

Combine $8$ and $\frac{8}{8}$ .

$\frac{3 h}{4} - 12 = \frac{8 \cdot 8}{8} + \frac{5}{8}$

Combine the numerators over the common denominator.

$\frac{3 h}{4} - 12 = \frac{8 \cdot 8 + 5}{8}$

Simplify the numerator.

Multiply $8$ by $8$ .

$\frac{3 h}{4} - 12 = \frac{64 + 5}{8}$

Add $64$ and $5$ .

$\frac{3 h}{4} - 12 = \frac{69}{8}$

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

Add $12$ to both sides of the equation.

$\frac{3 h}{4} = \frac{69}{8} + 12$

To write $12$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{3 h}{4} = \frac{69}{8} + 12 \cdot \frac{8}{8}$

Combine $12$ and $\frac{8}{8}$ .

$\frac{3 h}{4} = \frac{69}{8} + \frac{12 \cdot 8}{8}$

Combine the numerators over the common denominator.

$\frac{3 h}{4} = \frac{69 + 12 \cdot 8}{8}$

Simplify the numerator.

Multiply $12$ by $8$ .

$\frac{3 h}{4} = \frac{69 + 96}{8}$

Add $69$ and $96$ .

$\frac{3 h}{4} = \frac{165}{8}$

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 h}{4} = \frac{4}{3} \cdot \frac{165}{8}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 h}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 h}{4} = \frac{4}{3} \cdot \frac{165}{8}$

Rewrite the expression.

$\frac{1}{3} (3 h) = \frac{4}{3} \cdot \frac{165}{8}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 h$ .

$\frac{1}{3} (3 (h)) = \frac{4}{3} \cdot \frac{165}{8}$

Cancel the common factor.

$\frac{1}{3} (3 h) = \frac{4}{3} \cdot \frac{165}{8}$

Rewrite the expression.

$h = \frac{4}{3} \cdot \frac{165}{8}$

Simplify the right side.

Simplify $\frac{4}{3} \cdot \frac{165}{8}$ .

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$h = \frac{4}{3} \cdot \frac{165}{4 (2)}$

Cancel the common factor.

$h = \frac{4}{3} \cdot \frac{165}{4 \cdot 2}$

Rewrite the expression.

$h = \frac{1}{3} \cdot \frac{165}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $165$ .

$h = \frac{1}{3} \cdot \frac{3 (55)}{2}$

Cancel the common factor.

$h = \frac{1}{3} \cdot \frac{3 \cdot 55}{2}$

Rewrite the expression.

$h = \frac{55}{2}$

The result can be shown in multiple forms.

Exact Form:

$h = \frac{55}{2}$

Decimal Form:

$h = 27.5$

Mixed Number Form:

$h = 27 \frac{1}{2}$

Solve for h 3/4h-12=8 5/8

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