Basic Math Examples

$- \frac{2}{3} \cdot (\frac{6}{5} - 3 y) - \frac{4}{5} \cdot (\frac{1}{2} y - 2 \frac{1}{2})$

Step 1

Factor $- 1$ out of $- \frac{2}{3} \cdot (\frac{6}{5} - 3 y) - \frac{4}{5} \cdot (\frac{1}{2} y - 2 \frac{1}{2})$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Reorder $\frac{6}{5}$ and $- 3 y$ .

$- \frac{2}{3} \cdot (- 3 y + \frac{6}{5}) - \frac{4}{5} \cdot (\frac{1}{2} y - 2 \frac{1}{2})$

Step 1.1.2

Reorder $\frac{1}{2}$ and $y$ .

$- \frac{2}{3} \cdot (- 3 y + \frac{6}{5}) - \frac{4}{5} \cdot (y \frac{1}{2} - 2 \frac{1}{2})$

Step 1.2

Factor $- 1$ out of $- \frac{2}{3} \cdot (- 3 y + \frac{6}{5})$ .

$- (\frac{2}{3} \cdot (- 3 y + \frac{6}{5})) - \frac{4}{5} \cdot (y \frac{1}{2} - 2 \frac{1}{2})$

Step 1.3

Factor $- 1$ out of $- \frac{4}{5} \cdot (y \frac{1}{2} - 2 \frac{1}{2})$ .

$- (\frac{2}{3} \cdot (- 3 y + \frac{6}{5})) - (\frac{4}{5} \cdot (y \frac{1}{2} - 2 \frac{1}{2}))$

Step 1.4

Factor $- 1$ out of $- (\frac{2}{3} \cdot (- 3 y + \frac{6}{5})) - (\frac{4}{5} \cdot (y \frac{1}{2} - 2 \frac{1}{2}))$ .

$- (\frac{2}{3} \cdot (- 3 y + \frac{6}{5}) + \frac{4}{5} \cdot (y \frac{1}{2} - 2 \frac{1}{2}))$

Step 2

Factor.

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Step 2.1

Factor $\frac{1}{15}$ out of each term.

$- (\frac{1}{15} (- 30 y + 12 + 6 y - 30))$

Step 2.2

Remove unnecessary parentheses.

$- \frac{1}{15} (- 30 y + 12 + 6 y - 30)$

Step 3

Add $- 30 y$ and $6 y$ .

$- \frac{1}{15} \cdot (- 24 y + 12 - 30)$

Step 4

Subtract $30$ from $12$ .

$- \frac{1}{15} \cdot (- 24 y - 18)$

Step 5

Factor.

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Step 5.1

Factor $- 6$ out of $- 24 y - 18$ .

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Step 5.1.1

Factor $- 6$ out of $- 24 y$ .

$- \frac{1}{15} \cdot (- 6 (4 y) - 18)$

Step 5.1.2

Factor $- 6$ out of $- 18$ .

$- \frac{1}{15} \cdot (- 6 (4 y) - 6 (3))$

Step 5.1.3

Factor $- 6$ out of $- 6 (4 y) - 6 (3)$ .

$- \frac{1}{15} \cdot (- 6 (4 y + 3))$

Step 5.2

Remove unnecessary parentheses.

$- \frac{1}{15} \cdot - 6 (4 y + 3)$

Step 6

Combine exponents.

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Step 6.1

Multiply $- 6$ by $- 1$ .

$6 (\frac{1}{15}) (4 y + 3)$

Step 6.2

Combine $6$ and $\frac{1}{15}$ .

$\frac{6}{15} (4 y + 3)$

Step 7

Cancel the common factor of $6$ and $15$ .

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Step 7.1

Factor $3$ out of $6$ .

$\frac{3 (2)}{15} \cdot (4 y + 3)$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $15$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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