Algebra Examples

$2 \frac{2}{3} m + \frac{2}{3} m - m$

Step 1

Convert $2 \frac{2}{3}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(2 + \frac{2}{3}) m + \frac{2}{3} m - m$

Step 1.2

Add $2$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(2 \cdot \frac{3}{3} + \frac{2}{3}) m + \frac{2}{3} m - m$

Step 1.2.2

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

$(\frac{2 \cdot 3}{3} + \frac{2}{3}) m + \frac{2}{3} m - m$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 2}{3} m + \frac{2}{3} m - m$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $3$ .

$\frac{6 + 2}{3} m + \frac{2}{3} m - m$

Step 1.2.4.2

Add $6$ and $2$ .

$\frac{8}{3} m + \frac{2}{3} m - m$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{8}{3}$ and $m$ .

$\frac{8 m}{3} + \frac{2}{3} m - m$

Step 2.2

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

$\frac{8 m}{3} + \frac{2 m}{3} - m$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$- m + \frac{8 m + 2 m}{3}$

Step 3.2

Add $8 m$ and $2 m$ .

$- m + \frac{10 m}{3}$

Step 4

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

$- m \cdot \frac{3}{3} + \frac{10 m}{3}$

Step 5

Simplify terms.

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Step 5.1

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

$\frac{- m \cdot 3}{3} + \frac{10 m}{3}$

Step 5.2

Combine the numerators over the common denominator.

$\frac{- m \cdot 3 + 10 m}{3}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $m$ out of $- m \cdot 3 + 10 m$ .

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Step 6.1.1

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

$\frac{m (- 1 \cdot 3) + 10 m}{3}$

Step 6.1.2

Factor $m$ out of $10 m$ .

$\frac{m (- 1 \cdot 3) + m \cdot 10}{3}$

Step 6.1.3

Factor $m$ out of $m (- 1 \cdot 3) + m \cdot 10$ .

$\frac{m (- 1 \cdot 3 + 10)}{3}$

Step 6.2

Multiply $- 1$ by $3$ .

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

Step 6.3

Add $- 3$ and $10$ .

$\frac{m \cdot 7}{3}$

Step 7

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

$\frac{7 m}{3}$