Solve for m (3m)/4-m/12=7/8

$\frac{3 m}{4} - \frac{m}{12} = \frac{7}{8}$

Step 1

Simplify $\frac{3 m}{4} - \frac{m}{12}$ .

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

$\frac{3 m}{4} \cdot \frac{3}{3} - \frac{m}{12} = \frac{7}{8}$

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

Multiply $\frac{3 m}{4}$ by $\frac{3}{3}$ .

$\frac{3 m \cdot 3}{4 \cdot 3} - \frac{m}{12} = \frac{7}{8}$

Multiply $4$ by $3$ .

$\frac{3 m \cdot 3}{12} - \frac{m}{12} = \frac{7}{8}$

Combine the numerators over the common denominator.

$\frac{3 m \cdot 3 - m}{12} = \frac{7}{8}$

Simplify the numerator.

Factor $m$ out of $3 m \cdot 3 - m$ .

Factor $m$ out of $3 m \cdot 3$ .

$\frac{m (3 \cdot 3) - m}{12} = \frac{7}{8}$

Factor $m$ out of $- m$ .

$\frac{m (3 \cdot 3) + m \cdot - 1}{12} = \frac{7}{8}$

Factor $m$ out of $m (3 \cdot 3) + m \cdot - 1$ .

$\frac{m (3 \cdot 3 - 1)}{12} = \frac{7}{8}$

Multiply $3$ by $3$ .

$\frac{m (9 - 1)}{12} = \frac{7}{8}$

Subtract $1$ from $9$ .

$\frac{m \cdot 8}{12} = \frac{7}{8}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $8$ and $12$ .

Factor $4$ out of $m \cdot 8$ .

$\frac{4 (m \cdot 2)}{12} = \frac{7}{8}$

Cancel the common factors.

Factor $4$ out of $12$ .

$\frac{4 (m \cdot 2)}{4 (3)} = \frac{7}{8}$

Cancel the common factor.

$\frac{4 (m \cdot 2)}{4 \cdot 3} = \frac{7}{8}$

Rewrite the expression.

$\frac{m \cdot 2}{3} = \frac{7}{8}$

Move $2$ to the left of $m$ .

$\frac{2 m}{3} = \frac{7}{8}$

Step 2

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 m}{3} = \frac{3}{2} \cdot \frac{7}{8}$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 m}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 m}{3} = \frac{3}{2} \cdot \frac{7}{8}$

Rewrite the expression.

$\frac{1}{2} (2 m) = \frac{3}{2} \cdot \frac{7}{8}$

Cancel the common factor of $2$ .

Factor $2$ out of $2 m$ .

$\frac{1}{2} (2 (m)) = \frac{3}{2} \cdot \frac{7}{8}$

Cancel the common factor.

$\frac{1}{2} (2 m) = \frac{3}{2} \cdot \frac{7}{8}$

Rewrite the expression.

$m = \frac{3}{2} \cdot \frac{7}{8}$

Simplify the right side.

Multiply $\frac{3}{2} \cdot \frac{7}{8}$ .

Multiply $\frac{3}{2}$ by $\frac{7}{8}$ .

$m = \frac{3 \cdot 7}{2 \cdot 8}$

Multiply $3$ by $7$ .

$m = \frac{21}{2 \cdot 8}$

Multiply $2$ by $8$ .

$m = \frac{21}{16}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = \frac{21}{16}$

Decimal Form:

$m = 1.3125$

Mixed Number Form:

$m = 1 \frac{5}{16}$

Solve for m (3m)/4-m/12=7/8

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