Basic Math Examples

$(\frac{5}{8} \cdot \frac{16}{15}) y + (\frac{5}{8} \cdot \frac{32}{45}) z - \frac{5}{8} \cdot \frac{63}{25}$

Step 1

Factor $\frac{1}{8}$ out of each term.

$\frac{1}{8} (5 \cdot \frac{16}{15} y + 5 \cdot \frac{32}{45} z - 1 \cdot 5 \cdot \frac{63}{25})$

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Factor $5$ out of $15$ .

$\frac{1}{8} \cdot (5 \cdot \frac{16}{5 (3)} \cdot y + 5 \cdot \frac{32}{45} \cdot z - 1 \cdot 5 \cdot \frac{63}{25})$

Step 2.2

Cancel the common factor.

$\frac{1}{8} \cdot (5 \cdot \frac{16}{5 \cdot 3} \cdot y + 5 \cdot \frac{32}{45} \cdot z - 1 \cdot 5 \cdot \frac{63}{25})$

Step 2.3

Rewrite the expression.

$\frac{1}{8} \cdot (\frac{16}{3} \cdot y + 5 \cdot \frac{32}{45} \cdot z - 1 \cdot 5 \cdot \frac{63}{25})$

Step 3

Combine $\frac{16}{3}$ and $y$ .

$\frac{1}{8} \cdot (\frac{16 y}{3} + 5 \cdot \frac{32}{45} \cdot z - 1 \cdot 5 \cdot \frac{63}{25})$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Factor $5$ out of $45$ .

$\frac{1}{8} \cdot (\frac{16 y}{3} + 5 \cdot \frac{32}{5 (9)} \cdot z - 1 \cdot 5 \cdot \frac{63}{25})$

Step 4.2

Cancel the common factor.

$\frac{1}{8} \cdot (\frac{16 y}{3} + 5 \cdot \frac{32}{5 \cdot 9} \cdot z - 1 \cdot 5 \cdot \frac{63}{25})$

Step 4.3

Rewrite the expression.

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32}{9} \cdot z - 1 \cdot 5 \cdot \frac{63}{25})$

Step 5

Combine $\frac{32}{9}$ and $z$ .

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32 z}{9} - 1 \cdot 5 \cdot \frac{63}{25})$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Factor $5$ out of $- 1 \cdot 5$ .

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32 z}{9} + 5 \cdot - 1 \cdot \frac{63}{25})$

Step 6.2

Factor $5$ out of $25$ .

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32 z}{9} + 5 \cdot - 1 \cdot \frac{63}{5 (5)})$

Step 6.3

Cancel the common factor.

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32 z}{9} + 5 \cdot - 1 \cdot \frac{63}{5 \cdot 5})$

Step 6.4

Rewrite the expression.

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32 z}{9} - 1 \cdot \frac{63}{5})$

Step 7

Multiply $- 1$ by $\frac{63}{5}$ .

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32 z}{9} - 1 (\frac{63}{5}))$

Step 8

Rewrite $- 1 (\frac{63}{5})$ as $- (\frac{63}{5})$ .

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32 z}{9} - (\frac{63}{5}))$

Step 9

Multiply $- 1$ by $\frac{63}{5}$ .

$\frac{1}{8} \cdot (\frac{16 y}{3} + \frac{32 z}{9} - \frac{63}{5})$

Step 10

Factor.

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Step 10.1

Factor $\frac{1}{9}$ out of each term.

$\frac{1}{8} \cdot (\frac{1}{9} (48 y + 32 z - \frac{567}{5}))$

Step 10.2

Remove unnecessary parentheses.

$\frac{1}{8} \cdot \frac{1}{9} (48 y + 32 z - \frac{567}{5})$

Step 11

Combine exponents.

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Step 11.1

Multiply $\frac{1}{8}$ by $\frac{1}{9}$ .

$\frac{1}{8 \cdot 9} (48 y + 32 z - \frac{567}{5})$

Step 11.2

Multiply $8$ by $9$ .

$\frac{1}{72} (48 y + 32 z - \frac{567}{5})$