Algebra Examples

$\frac{3}{10} (4 m - 8) + 9 m$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{3}{10} (4 m) + \frac{3}{10} \cdot - 8 + 9 m$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $10$ .

$\frac{3}{2 (5)} (4 m) + \frac{3}{10} \cdot - 8 + 9 m$

Step 1.2.2

Factor $2$ out of $4 m$ .

$\frac{3}{2 (5)} (2 (2 m)) + \frac{3}{10} \cdot - 8 + 9 m$

Step 1.2.3

Cancel the common factor.

$\frac{3}{2 \cdot 5} (2 (2 m)) + \frac{3}{10} \cdot - 8 + 9 m$

Step 1.2.4

Rewrite the expression.

$\frac{3}{5} (2 m) + \frac{3}{10} \cdot - 8 + 9 m$

Step 1.3

Combine $2$ and $\frac{3}{5}$ .

$\frac{2 \cdot 3}{5} m + \frac{3}{10} \cdot - 8 + 9 m$

Step 1.4

Multiply $2$ by $3$ .

$\frac{6}{5} m + \frac{3}{10} \cdot - 8 + 9 m$

Step 1.5

Combine $\frac{6}{5}$ and $m$ .

$\frac{6 m}{5} + \frac{3}{10} \cdot - 8 + 9 m$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $10$ .

$\frac{6 m}{5} + \frac{3}{2 (5)} \cdot - 8 + 9 m$

Step 1.6.2

Factor $2$ out of $- 8$ .

$\frac{6 m}{5} + \frac{3}{2 \cdot 5} \cdot (2 \cdot - 4) + 9 m$

Step 1.6.3

Cancel the common factor.

$\frac{6 m}{5} + \frac{3}{2 \cdot 5} \cdot (2 \cdot - 4) + 9 m$

Step 1.6.4

Rewrite the expression.

$\frac{6 m}{5} + \frac{3}{5} \cdot - 4 + 9 m$

Step 1.7

Combine $\frac{3}{5}$ and $- 4$ .

$\frac{6 m}{5} + \frac{3 \cdot - 4}{5} + 9 m$

Step 1.8

Multiply $3$ by $- 4$ .

$\frac{6 m}{5} + \frac{- 12}{5} + 9 m$

Step 1.9

Move the negative in front of the fraction.

$\frac{6 m}{5} - \frac{12}{5} + 9 m$

Step 2

To write $9 m$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 m}{5} + 9 m \cdot \frac{5}{5} - \frac{12}{5}$

Step 3

Combine $9 m$ and $\frac{5}{5}$ .

$\frac{6 m}{5} + \frac{9 m \cdot 5}{5} - \frac{12}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 m + 9 m \cdot 5}{5} - \frac{12}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 m + 9 m \cdot 5 - 12}{5}$

Step 6

Multiply $5$ by $9$ .

$\frac{6 m + 45 m - 12}{5}$

Step 7

Add $6 m$ and $45 m$ .

$\frac{51 m - 12}{5}$

Step 8

Factor $3$ out of $51 m - 12$ .

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Step 8.1

Factor $3$ out of $51 m$ .

$\frac{3 (17 m) - 12}{5}$

Step 8.2

Factor $3$ out of $- 12$ .

$\frac{3 (17 m) + 3 (- 4)}{5}$

Step 8.3

Factor $3$ out of $3 (17 m) + 3 (- 4)$ .

$\frac{3 (17 m - 4)}{5}$