Pre-Algebra Examples

$- \frac{2}{3} \cdot (5 - 2 i) - 3 (9 - 2 i) - (7 - 2 i)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{2}{3} \cdot 5 - \frac{2}{3} (- 2 i) - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.2

Multiply $- \frac{2}{3} \cdot 5$ .

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Step 1.2.1

Multiply $5$ by $- 1$ .

$- 5 (\frac{2}{3}) - \frac{2}{3} (- 2 i) - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.2.2

Combine $- 5$ and $\frac{2}{3}$ .

$\frac{- 5 \cdot 2}{3} - \frac{2}{3} (- 2 i) - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.2.3

Multiply $- 5$ by $2$ .

$\frac{- 10}{3} - \frac{2}{3} (- 2 i) - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.3

Multiply $- \frac{2}{3} (- 2 i)$ .

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Step 1.3.1

Multiply $- 2$ by $- 1$ .

$\frac{- 10}{3} + 2 (\frac{2}{3}) i - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.3.2

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

$\frac{- 10}{3} + \frac{2 \cdot 2}{3} i - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.3.3

Multiply $2$ by $2$ .

$\frac{- 10}{3} + \frac{4}{3} i - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.3.4

Combine $\frac{4}{3}$ and $i$ .

$\frac{- 10}{3} + \frac{4 i}{3} - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.4

Move the negative in front of the fraction.

$- \frac{10}{3} + \frac{4 i}{3} - 3 (9 - 2 i) - (7 - 2 i)$

Step 1.5

Apply the distributive property.

$- \frac{10}{3} + \frac{4 i}{3} - 3 \cdot 9 - 3 (- 2 i) - (7 - 2 i)$

Step 1.6

Multiply $- 3$ by $9$ .

$- \frac{10}{3} + \frac{4 i}{3} - 27 - 3 (- 2 i) - (7 - 2 i)$

Step 1.7

Multiply $- 2$ by $- 3$ .

$- \frac{10}{3} + \frac{4 i}{3} - 27 + 6 i - (7 - 2 i)$

Step 1.8

Apply the distributive property.

$- \frac{10}{3} + \frac{4 i}{3} - 27 + 6 i - 1 \cdot 7 - (- 2 i)$

Step 1.9

Multiply $- 1$ by $7$ .

$- \frac{10}{3} + \frac{4 i}{3} - 27 + 6 i - 7 - (- 2 i)$

Step 1.10

Multiply $- 2$ by $- 1$ .

$- \frac{10}{3} + \frac{4 i}{3} - 27 + 6 i - 7 + 2 i$

Step 2

To write $- 27$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{10}{3} - 27 \cdot \frac{3}{3} + \frac{4 i}{3} + 6 i - 7 + 2 i$

Step 3

Combine $- 27$ and $\frac{3}{3}$ .

$- \frac{10}{3} + \frac{- 27 \cdot 3}{3} + \frac{4 i}{3} + 6 i - 7 + 2 i$

Step 4

Combine the numerators over the common denominator.

$\frac{- 10 - 27 \cdot 3}{3} + \frac{4 i}{3} + 6 i - 7 + 2 i$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 27$ by $3$ .

$\frac{- 10 - 81}{3} + \frac{4 i}{3} + 6 i - 7 + 2 i$

Step 5.2

Subtract $81$ from $- 10$ .

$\frac{- 91}{3} + \frac{4 i}{3} + 6 i - 7 + 2 i$

Step 6

Move the negative in front of the fraction.

$- \frac{91}{3} + \frac{4 i}{3} + 6 i - 7 + 2 i$

Step 7

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{91}{3} - 7 \cdot \frac{3}{3} + \frac{4 i}{3} + 6 i + 2 i$

Step 8

Combine $- 7$ and $\frac{3}{3}$ .

$- \frac{91}{3} + \frac{- 7 \cdot 3}{3} + \frac{4 i}{3} + 6 i + 2 i$

Step 9

Combine the numerators over the common denominator.

$\frac{- 91 - 7 \cdot 3}{3} + \frac{4 i}{3} + 6 i + 2 i$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $- 7$ by $3$ .

$\frac{- 91 - 21}{3} + \frac{4 i}{3} + 6 i + 2 i$

Step 10.2

Subtract $21$ from $- 91$ .

$\frac{- 112}{3} + \frac{4 i}{3} + 6 i + 2 i$

Step 11

Move the negative in front of the fraction.

$- \frac{112}{3} + \frac{4 i}{3} + 6 i + 2 i$

Step 12

To write $6 i$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{112}{3} + \frac{4 i}{3} + 6 i \cdot \frac{3}{3} + 2 i$

Step 13

Combine $6 i$ and $\frac{3}{3}$ .

$- \frac{112}{3} + \frac{4 i}{3} + \frac{6 i \cdot 3}{3} + 2 i$

Step 14

Combine the numerators over the common denominator.

$- \frac{112}{3} + \frac{22 i}{3} + 2 i$

Step 15

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

$- \frac{112}{3} + \frac{22 i}{3} + 2 i \cdot \frac{3}{3}$

Step 16

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

$- \frac{112}{3} + \frac{22 i}{3} + \frac{2 i \cdot 3}{3}$

Step 17

Combine the numerators over the common denominator.

$- \frac{112}{3} + \frac{28 i}{3}$