Basic Math Examples

$\frac{3}{8} \cdot (\frac{16}{9} y + \frac{32}{27} z - \frac{40}{9})$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{16}{9}$ and $y$ .

$\frac{3}{8} \cdot (\frac{16 y}{9} + \frac{32}{27} z - \frac{40}{9})$

Step 1.2

Combine $\frac{32}{27}$ and $z$ .

$\frac{3}{8} \cdot (\frac{16 y}{9} + \frac{32 z}{27} - \frac{40}{9})$

Step 2

Apply the distributive property.

$\frac{3}{8} \cdot \frac{16 y}{9} + \frac{3}{8} \cdot \frac{32 z}{27} + \frac{3}{8} (- \frac{40}{9})$

Step 3

Simplify.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Factor $3$ out of $9$ .

$\frac{3}{8} \cdot \frac{16 y}{3 (3)} + \frac{3}{8} \cdot \frac{32 z}{27} + \frac{3}{8} (- \frac{40}{9})$

Step 3.1.2

Cancel the common factor.

$\frac{3}{8} \cdot \frac{16 y}{3 \cdot 3} + \frac{3}{8} \cdot \frac{32 z}{27} + \frac{3}{8} (- \frac{40}{9})$

Step 3.1.3

Rewrite the expression.

$\frac{1}{8} \cdot \frac{16 y}{3} + \frac{3}{8} \cdot \frac{32 z}{27} + \frac{3}{8} (- \frac{40}{9})$

Step 3.2

Cancel the common factor of $8$ .

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Step 3.2.1

Factor $8$ out of $16 y$ .

$\frac{1}{8} \cdot \frac{8 (2 y)}{3} + \frac{3}{8} \cdot \frac{32 z}{27} + \frac{3}{8} (- \frac{40}{9})$

Step 3.2.2

Cancel the common factor.

$\frac{1}{8} \cdot \frac{8 (2 y)}{3} + \frac{3}{8} \cdot \frac{32 z}{27} + \frac{3}{8} (- \frac{40}{9})$

Step 3.2.3

Rewrite the expression.

$\frac{2 y}{3} + \frac{3}{8} \cdot \frac{32 z}{27} + \frac{3}{8} (- \frac{40}{9})$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Factor $3$ out of $27$ .

$\frac{2 y}{3} + \frac{3}{8} \cdot \frac{32 z}{3 (9)} + \frac{3}{8} (- \frac{40}{9})$

Step 3.3.2

Cancel the common factor.

$\frac{2 y}{3} + \frac{3}{8} \cdot \frac{32 z}{3 \cdot 9} + \frac{3}{8} (- \frac{40}{9})$

Step 3.3.3

Rewrite the expression.

$\frac{2 y}{3} + \frac{1}{8} \cdot \frac{32 z}{9} + \frac{3}{8} (- \frac{40}{9})$

Step 3.4

Cancel the common factor of $8$ .

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Step 3.4.1

Factor $8$ out of $32 z$ .

$\frac{2 y}{3} + \frac{1}{8} \cdot \frac{8 (4 z)}{9} + \frac{3}{8} (- \frac{40}{9})$

Step 3.4.2

Cancel the common factor.

$\frac{2 y}{3} + \frac{1}{8} \cdot \frac{8 (4 z)}{9} + \frac{3}{8} (- \frac{40}{9})$

Step 3.4.3

Rewrite the expression.

$\frac{2 y}{3} + \frac{4 z}{9} + \frac{3}{8} (- \frac{40}{9})$

Step 3.5

Cancel the common factor of $3$ .

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Step 3.5.1

Move the leading negative in $- \frac{40}{9}$ into the numerator.

$\frac{2 y}{3} + \frac{4 z}{9} + \frac{3}{8} \cdot \frac{- 40}{9}$

Step 3.5.2

Factor $3$ out of $9$ .

$\frac{2 y}{3} + \frac{4 z}{9} + \frac{3}{8} \cdot \frac{- 40}{3 (3)}$

Step 3.5.3

Cancel the common factor.

$\frac{2 y}{3} + \frac{4 z}{9} + \frac{3}{8} \cdot \frac{- 40}{3 \cdot 3}$

Step 3.5.4

Rewrite the expression.

$\frac{2 y}{3} + \frac{4 z}{9} + \frac{1}{8} \cdot \frac{- 40}{3}$

Step 3.6

Cancel the common factor of $8$ .

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Step 3.6.1

Factor $8$ out of $- 40$ .

$\frac{2 y}{3} + \frac{4 z}{9} + \frac{1}{8} \cdot \frac{8 (- 5)}{3}$

Step 3.6.2

Cancel the common factor.

$\frac{2 y}{3} + \frac{4 z}{9} + \frac{1}{8} \cdot \frac{8 \cdot - 5}{3}$

Step 3.6.3

Rewrite the expression.

$\frac{2 y}{3} + \frac{4 z}{9} + \frac{- 5}{3}$

Step 4

Move the negative in front of the fraction.

$\frac{2 y}{3} + \frac{4 z}{9} - \frac{5}{3}$