Pre-Algebra Examples

$\frac{3 + 5 i}{7} + \frac{- 5 + 7 i}{7} + (\frac{- 8 i}{7} + \frac{1}{2})$

Step 1

Simplify terms.

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Step 1.1

Remove parentheses.

$\frac{3 + 5 i}{7} + \frac{- 5 + 7 i}{7} + \frac{- 8 i}{7} + \frac{1}{2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3 + 5 i - 5 + 7 i - 8 i}{7} + \frac{1}{2}$

Step 1.3

Subtract $5$ from $3$ .

$\frac{- 2 + 5 i + 7 i - 8 i}{7} + \frac{1}{2}$

Step 1.4

Add $5 i$ and $7 i$ .

$\frac{- 2 + 12 i - 8 i}{7} + \frac{1}{2}$

Step 1.5

Subtract $8 i$ from $12 i$ .

$\frac{- 2 + 4 i}{7} + \frac{1}{2}$

Step 2

Simplify each term.

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Step 2.1

Split the fraction $\frac{- 2 + 4 i}{7}$ into two fractions.

$\frac{- 2}{7} + \frac{4 i}{7} + \frac{1}{2}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{2}{7} + \frac{4 i}{7} + \frac{1}{2}$

Step 3

To write $- \frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{2}{7} \cdot \frac{2}{2} + \frac{1}{2} + \frac{4 i}{7}$

Step 4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{2}{7} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{7}{7} + \frac{4 i}{7}$

Step 5

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

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

$- \frac{2 \cdot 2}{7 \cdot 2} + \frac{1}{2} \cdot \frac{7}{7} + \frac{4 i}{7}$

Step 5.2

Multiply $7$ by $2$ .

$- \frac{2 \cdot 2}{14} + \frac{1}{2} \cdot \frac{7}{7} + \frac{4 i}{7}$

Step 5.3

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$- \frac{2 \cdot 2}{14} + \frac{7}{2 \cdot 7} + \frac{4 i}{7}$

Step 5.4

Multiply $2$ by $7$ .

$- \frac{2 \cdot 2}{14} + \frac{7}{14} + \frac{4 i}{7}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 2 + 7}{14} + \frac{4 i}{7}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 2$ by $2$ .

$\frac{- 4 + 7}{14} + \frac{4 i}{7}$

Step 7.2

Add $- 4$ and $7$ .

$\frac{3}{14} + \frac{4 i}{7}$