Algebra Examples

$2 (\frac{5}{2} - 3) + 6 (\frac{1}{3} + \frac{5}{2})$

Step 1

Simplify each term.

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Step 1.1

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

$2 (\frac{5}{2} - 3 \cdot \frac{2}{2}) + 6 (\frac{1}{3} + \frac{5}{2})$

Step 1.2

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

$2 (\frac{5}{2} + \frac{- 3 \cdot 2}{2}) + 6 (\frac{1}{3} + \frac{5}{2})$

Step 1.3

Combine the numerators over the common denominator.

$2 \frac{5 - 3 \cdot 2}{2} + 6 (\frac{1}{3} + \frac{5}{2})$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $- 3$ by $2$ .

$2 \frac{5 - 6}{2} + 6 (\frac{1}{3} + \frac{5}{2})$

Step 1.4.2

Subtract $6$ from $5$ .

$2 (\frac{- 1}{2}) + 6 (\frac{1}{3} + \frac{5}{2})$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Cancel the common factor.

$2 (\frac{- 1}{2}) + 6 (\frac{1}{3} + \frac{5}{2})$

Step 1.5.2

Rewrite the expression.

$- 1 + 6 (\frac{1}{3} + \frac{5}{2})$

Step 1.6

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 1 + 6 (\frac{1}{3} \cdot \frac{2}{2} + \frac{5}{2})$

Step 1.7

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 1 + 6 (\frac{1}{3} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{3}{3})$

Step 1.8

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.8.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$- 1 + 6 (\frac{2}{3 \cdot 2} + \frac{5}{2} \cdot \frac{3}{3})$

Step 1.8.2

Multiply $3$ by $2$ .

$- 1 + 6 (\frac{2}{6} + \frac{5}{2} \cdot \frac{3}{3})$

Step 1.8.3

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

$- 1 + 6 (\frac{2}{6} + \frac{5 \cdot 3}{2 \cdot 3})$

Step 1.8.4

Multiply $2$ by $3$ .

$- 1 + 6 (\frac{2}{6} + \frac{5 \cdot 3}{6})$

Step 1.9

Combine the numerators over the common denominator.

$- 1 + 6 \frac{2 + 5 \cdot 3}{6}$

Step 1.10

Simplify the numerator.

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Step 1.10.1

Multiply $5$ by $3$ .

$- 1 + 6 \frac{2 + 15}{6}$

Step 1.10.2

Add $2$ and $15$ .

$- 1 + 6 (\frac{17}{6})$

Step 1.11

Cancel the common factor of $6$ .

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Step 1.11.1

Cancel the common factor.

$- 1 + 6 (\frac{17}{6})$

Step 1.11.2

Rewrite the expression.

$- 1 + 17$

Step 2

Add $- 1$ and $17$ .

$16$