Algebra Examples

$\frac{\frac{m}{5} - \frac{1}{6}}{\frac{1}{3}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{m}{5} - \frac{1}{6}) \cdot 3$

Step 2

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

$(\frac{m}{5} \cdot \frac{6}{6} - \frac{1}{6}) \cdot 3$

Step 3

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{m}{5} \cdot \frac{6}{6} - \frac{1}{6} \cdot \frac{5}{5}) \cdot 3$

Step 4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{m}{5}$ by $\frac{6}{6}$ .

$(\frac{m \cdot 6}{5 \cdot 6} - \frac{1}{6} \cdot \frac{5}{5}) \cdot 3$

Step 4.2

Multiply $5$ by $6$ .

$(\frac{m \cdot 6}{30} - \frac{1}{6} \cdot \frac{5}{5}) \cdot 3$

Step 4.3

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$(\frac{m \cdot 6}{30} - \frac{5}{6 \cdot 5}) \cdot 3$

Step 4.4

Multiply $6$ by $5$ .

$(\frac{m \cdot 6}{30} - \frac{5}{30}) \cdot 3$

Step 5

Combine the numerators over the common denominator.

$\frac{m \cdot 6 - 5}{30} \cdot 3$

Step 6

Move $6$ to the left of $m$ .

$\frac{6 m - 5}{30} \cdot 3$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $30$ .

$\frac{6 m - 5}{3 (10)} \cdot 3$

Step 7.2

Cancel the common factor.

$\frac{6 m - 5}{3 \cdot 10} \cdot 3$

Step 7.3

Rewrite the expression.

$\frac{6 m - 5}{10}$