Algebra Examples

$(\frac{4}{3}) (\frac{3}{5} + \frac{7}{2} - 2)$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

$\frac{4}{3} (\frac{3}{5} \cdot \frac{2}{2} + \frac{7}{2} - 2)$

Step 1.2

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

$\frac{4}{3} (\frac{3 \cdot 2}{5 \cdot 2} + \frac{7}{2} - 2)$

Step 1.3

Multiply $\frac{7}{2}$ by $\frac{5}{5}$ .

$\frac{4}{3} (\frac{3 \cdot 2}{5 \cdot 2} + \frac{7}{2} \cdot \frac{5}{5} - 2)$

Step 1.4

Multiply $\frac{7}{2}$ by $\frac{5}{5}$ .

$\frac{4}{3} (\frac{3 \cdot 2}{5 \cdot 2} + \frac{7 \cdot 5}{2 \cdot 5} - 2)$

Step 1.5

Write $- 2$ as a fraction with denominator $1$ .

$\frac{4}{3} (\frac{3 \cdot 2}{5 \cdot 2} + \frac{7 \cdot 5}{2 \cdot 5} + \frac{- 2}{1})$

Step 1.6

Multiply $\frac{- 2}{1}$ by $\frac{10}{10}$ .

$\frac{4}{3} (\frac{3 \cdot 2}{5 \cdot 2} + \frac{7 \cdot 5}{2 \cdot 5} + \frac{- 2}{1} \cdot \frac{10}{10})$

Step 1.7

Multiply $\frac{- 2}{1}$ by $\frac{10}{10}$ .

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

Step 1.8

Reorder the factors of $5 \cdot 2$ .

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

Step 1.9

Multiply $2$ by $5$ .

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

Step 1.10

Multiply $2$ by $5$ .

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

Step 2

Combine the numerators over the common denominator.

$\frac{4}{3} \cdot \frac{3 \cdot 2 + 7 \cdot 5 - 2 \cdot 10}{10}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $2$ .

$\frac{4}{3} \cdot \frac{6 + 7 \cdot 5 - 2 \cdot 10}{10}$

Step 3.2

Multiply $7$ by $5$ .

$\frac{4}{3} \cdot \frac{6 + 35 - 2 \cdot 10}{10}$

Step 3.3

Multiply $- 2$ by $10$ .

$\frac{4}{3} \cdot \frac{6 + 35 - 20}{10}$

Step 4

Simplify terms.

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Step 4.1

Add $6$ and $35$ .

$\frac{4}{3} \cdot \frac{41 - 20}{10}$

Step 4.2

Subtract $20$ from $41$ .

$\frac{4}{3} \cdot \frac{21}{10}$

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{3} \cdot \frac{21}{10}$

Step 4.3.2

Factor $2$ out of $10$ .

$\frac{2 \cdot 2}{3} \cdot \frac{21}{2 \cdot 5}$

Step 4.3.3

Cancel the common factor.

$\frac{2 \cdot 2}{3} \cdot \frac{21}{2 \cdot 5}$

Step 4.3.4

Rewrite the expression.

$\frac{2}{3} \cdot \frac{21}{5}$

Step 4.4

Cancel the common factor of $3$ .

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Step 4.4.1

Factor $3$ out of $21$ .

$\frac{2}{3} \cdot \frac{3 (7)}{5}$

Step 4.4.2

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 \cdot 7}{5}$

Step 4.4.3

Rewrite the expression.

$2 (\frac{7}{5})$

Step 4.5

Combine $2$ and $\frac{7}{5}$ .

$\frac{2 \cdot 7}{5}$

Step 4.6

Multiply $2$ by $7$ .

$\frac{14}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{14}{5}$

Decimal Form:

$2.8$

Mixed Number Form:

$2 \frac{4}{5}$