Algebra Examples

$\frac{7}{8} m + \frac{9}{10} - 2 m - \frac{3}{5}$

Step 1

Combine $\frac{7}{8}$ and $m$ .

$\frac{7 m}{8} + \frac{9}{10} - 2 m - \frac{3}{5}$

Step 2

To write $- 2 m$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{7 m}{8} - 2 m \cdot \frac{8}{8} + \frac{9}{10} - \frac{3}{5}$

Step 3

Combine $- 2 m$ and $\frac{8}{8}$ .

$\frac{7 m}{8} + \frac{- 2 m \cdot 8}{8} + \frac{9}{10} - \frac{3}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 m - 2 m \cdot 8}{8} + \frac{9}{10} - \frac{3}{5}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{7 m - 2 m \cdot 8}{8}$ by $\frac{5}{5}$ .

$\frac{7 m - 2 m \cdot 8}{8} \cdot \frac{5}{5} + \frac{9}{10} - \frac{3}{5}$

Step 5.2

Multiply $\frac{7 m - 2 m \cdot 8}{8}$ by $\frac{5}{5}$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{8 \cdot 5} + \frac{9}{10} - \frac{3}{5}$

Step 5.3

Multiply $\frac{9}{10}$ by $\frac{4}{4}$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{8 \cdot 5} + \frac{9}{10} \cdot \frac{4}{4} - \frac{3}{5}$

Step 5.4

Multiply $\frac{9}{10}$ by $\frac{4}{4}$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{8 \cdot 5} + \frac{9 \cdot 4}{10 \cdot 4} - \frac{3}{5}$

Step 5.5

Multiply $\frac{3}{5}$ by $\frac{8}{8}$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{8 \cdot 5} + \frac{9 \cdot 4}{10 \cdot 4} - (\frac{3}{5} \cdot \frac{8}{8})$

Step 5.6

Multiply $\frac{3}{5}$ by $\frac{8}{8}$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{8 \cdot 5} + \frac{9 \cdot 4}{10 \cdot 4} - \frac{3 \cdot 8}{5 \cdot 8}$

Step 5.7

Reorder the factors of $8 \cdot 5$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{5 \cdot 8} + \frac{9 \cdot 4}{10 \cdot 4} - \frac{3 \cdot 8}{5 \cdot 8}$

Step 5.8

Multiply $5$ by $8$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{40} + \frac{9 \cdot 4}{10 \cdot 4} - \frac{3 \cdot 8}{5 \cdot 8}$

Step 5.9

Reorder the factors of $10 \cdot 4$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{40} + \frac{9 \cdot 4}{4 \cdot 10} - \frac{3 \cdot 8}{5 \cdot 8}$

Step 5.10

Multiply $4$ by $10$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{40} + \frac{9 \cdot 4}{40} - \frac{3 \cdot 8}{5 \cdot 8}$

Step 5.11

Multiply $5$ by $8$ .

$\frac{(7 m - 2 m \cdot 8) \cdot 5}{40} + \frac{9 \cdot 4}{40} - \frac{3 \cdot 8}{40}$

Step 6

Combine the numerators over the common denominator.

$\frac{(7 m - 2 m \cdot 8) \cdot 5 + 9 \cdot 4 - 3 \cdot 8}{40}$

Step 7

Simplify each term.

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Step 7.1

Multiply $8$ by $- 2$ .

$\frac{(7 m - 16 m) \cdot 5 + 9 \cdot 4 - 3 \cdot 8}{40}$

Step 7.2

Subtract $16 m$ from $7 m$ .

$\frac{- 9 m \cdot 5 + 9 \cdot 4 - 3 \cdot 8}{40}$

Step 7.3

Multiply $5$ by $- 9$ .

$\frac{- 45 m + 9 \cdot 4 - 3 \cdot 8}{40}$

Step 7.4

Multiply $9$ by $4$ .

$\frac{- 45 m + 36 - 3 \cdot 8}{40}$

Step 7.5

Multiply $- 3$ by $8$ .

$\frac{- 45 m + 36 - 24}{40}$

Step 8

Simplify with factoring out.

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Step 8.1

Subtract $24$ from $36$ .

$\frac{- 45 m + 12}{40}$

Step 8.2

Factor $3$ out of $- 45 m + 12$ .

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Step 8.2.1

Factor $3$ out of $- 45 m$ .

$\frac{3 (- 15 m) + 12}{40}$

Step 8.2.2

Factor $3$ out of $12$ .

$\frac{3 (- 15 m) + 3 (4)}{40}$

Step 8.2.3

Factor $3$ out of $3 (- 15 m) + 3 (4)$ .

$\frac{3 (- 15 m + 4)}{40}$

Step 8.3

Factor $- 1$ out of $- 15 m$ .

$\frac{3 (- (15 m) + 4)}{40}$

Step 8.4

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{3 (- (15 m) - 1 (- 4))}{40}$

Step 8.5

Factor $- 1$ out of $- (15 m) - 1 (- 4)$ .

$\frac{3 (- (15 m - 4))}{40}$

Step 8.6

Simplify the expression.

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Step 8.6.1

Rewrite $- (15 m - 4)$ as $- 1 (15 m - 4)$ .

$\frac{3 (- 1 (15 m - 4))}{40}$

Step 8.6.2

Move the negative in front of the fraction.

$- \frac{3 (15 m - 4)}{40}$