Algebra Examples

$- 4 n + \frac{1}{3} m + 4 n - \frac{4}{5} m$

Step 1

Combine the opposite terms in $- 4 n + \frac{1}{3} m + 4 n - \frac{4}{5} m$ .

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Step 1.1

Add $- 4 n$ and $4 n$ .

$\frac{1}{3} m + 0 - \frac{4}{5} m$

Step 1.2

Add $\frac{1}{3} m$ and $0$ .

$\frac{1}{3} m - \frac{4}{5} m$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{1}{3}$ and $m$ .

$\frac{m}{3} - \frac{4}{5} m$

Step 2.2

Combine $m$ and $\frac{4}{5}$ .

$\frac{m}{3} - \frac{m \cdot 4}{5}$

Step 2.3

Move $4$ to the left of $m$ .

$\frac{m}{3} - \frac{4 m}{5}$

Step 3

To write $\frac{m}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{m}{3} \cdot \frac{5}{5} - \frac{4 m}{5}$

Step 4

To write $- \frac{4 m}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{m}{3} \cdot \frac{5}{5} - \frac{4 m}{5} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

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

$\frac{m \cdot 5}{3 \cdot 5} - \frac{4 m}{5} \cdot \frac{3}{3}$

Step 5.2

Multiply $3$ by $5$ .

$\frac{m \cdot 5}{15} - \frac{4 m}{5} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{4 m}{5}$ by $\frac{3}{3}$ .

$\frac{m \cdot 5}{15} - \frac{4 m \cdot 3}{5 \cdot 3}$

Step 5.4

Multiply $5$ by $3$ .

$\frac{m \cdot 5}{15} - \frac{4 m \cdot 3}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{m \cdot 5 - 4 m \cdot 3}{15}$

Step 7

Simplify the numerator.

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Step 7.1

Factor $m$ out of $m \cdot 5 - 4 m \cdot 3$ .

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Step 7.1.1

Factor $m$ out of $m \cdot 5$ .

$\frac{m (5) - 4 m \cdot 3}{15}$

Step 7.1.2

Factor $m$ out of $- 4 m \cdot 3$ .

$\frac{m (5) + m (- 4 \cdot 3)}{15}$

Step 7.1.3

Factor $m$ out of $m (5) + m (- 4 \cdot 3)$ .

$\frac{m (5 - 4 \cdot 3)}{15}$

Step 7.2

Multiply $- 4$ by $3$ .

$\frac{m (5 - 12)}{15}$

Step 7.3

Subtract $12$ from $5$ .

$\frac{m \cdot - 7}{15}$

Step 8

Simplify the expression.

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Step 8.1

Move $- 7$ to the left of $m$ .

$\frac{- 7 \cdot m}{15}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{7 m}{15}$