Basic Math Examples

$(- \frac{1}{2} + 3) - (15 - 7 i)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{1}{2} + 3 - 1 \cdot 15 - (- 7 i)$

Step 1.2

Multiply $- 1$ by $15$ .

$- \frac{1}{2} + 3 - 15 - (- 7 i)$

Step 1.3

Multiply $- 7$ by $- 1$ .

$- \frac{1}{2} + 3 - 15 + 7 i$

Step 2

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

$- \frac{1}{2} + 3 \cdot \frac{2}{2} - 15 + 7 i$

Step 3

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

$- \frac{1}{2} + \frac{3 \cdot 2}{2} - 15 + 7 i$

Step 4

Combine the numerators over the common denominator.

$\frac{- 1 + 3 \cdot 2}{2} - 15 + 7 i$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $2$ .

$\frac{- 1 + 6}{2} - 15 + 7 i$

Step 5.2

Add $- 1$ and $6$ .

$\frac{5}{2} - 15 + 7 i$

Step 6

To write $- 15$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2} - 15 \cdot \frac{2}{2} + 7 i$

Step 7

Combine $- 15$ and $\frac{2}{2}$ .

$\frac{5}{2} + \frac{- 15 \cdot 2}{2} + 7 i$

Step 8

Combine the numerators over the common denominator.

$\frac{5 - 15 \cdot 2}{2} + 7 i$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 15$ by $2$ .

$\frac{5 - 30}{2} + 7 i$

Step 9.2

Subtract $30$ from $5$ .

$\frac{- 25}{2} + 7 i$

Step 10

Move the negative in front of the fraction.

$- \frac{25}{2} + 7 i$