Basic Math Examples

$- \frac{7}{12} z = \frac{32}{15}$

Step 1

Multiply both sides of the equation by $- \frac{12}{7}$ .

$- \frac{12}{7} (- \frac{7}{12} z) = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- \frac{12}{7} (- \frac{7}{12} z)$ .

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Step 2.1.1.1

Combine $z$ and $\frac{7}{12}$ .

$- \frac{12}{7} (- \frac{z \cdot 7}{12}) = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.2

Cancel the common factor of $12$ .

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Step 2.1.1.2.1

Move the leading negative in $- \frac{12}{7}$ into the numerator.

$\frac{- 12}{7} (- \frac{z \cdot 7}{12}) = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.2.2

Move the leading negative in $- \frac{z \cdot 7}{12}$ into the numerator.

$\frac{- 12}{7} \cdot \frac{- z \cdot 7}{12} = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.2.3

Factor $12$ out of $- 12$ .

$\frac{12 (- 1)}{7} \cdot \frac{- z \cdot 7}{12} = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{12 \cdot - 1}{7} \cdot \frac{- z \cdot 7}{12} = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{- 1}{7} (- z \cdot 7) = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.3

Cancel the common factor of $7$ .

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Step 2.1.1.3.1

Factor $7$ out of $- z \cdot 7$ .

$\frac{- 1}{7} (7 \cdot (- z)) = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{- 1}{7} (7 \cdot (- z)) = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.3.3

Rewrite the expression.

$- - z = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.1.1.4.2

Multiply $z$ by $1$ .

$z = - \frac{12}{7} \cdot \frac{32}{15}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{12}{7} \cdot \frac{32}{15}$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{12}{7}$ into the numerator.

$z = \frac{- 12}{7} \cdot \frac{32}{15}$

Step 2.2.1.1.2

Factor $3$ out of $- 12$ .

$z = \frac{3 (- 4)}{7} \cdot \frac{32}{15}$

Step 2.2.1.1.3

Factor $3$ out of $15$ .

$z = \frac{3 \cdot - 4}{7} \cdot \frac{32}{3 \cdot 5}$

Step 2.2.1.1.4

Cancel the common factor.

$z = \frac{3 \cdot - 4}{7} \cdot \frac{32}{3 \cdot 5}$

Step 2.2.1.1.5

Rewrite the expression.

$z = \frac{- 4}{7} \cdot \frac{32}{5}$

Step 2.2.1.2

Multiply $\frac{- 4}{7}$ by $\frac{32}{5}$ .

$z = \frac{- 4 \cdot 32}{7 \cdot 5}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $- 4$ by $32$ .

$z = \frac{- 128}{7 \cdot 5}$

Step 2.2.1.3.2

Multiply $7$ by $5$ .

$z = \frac{- 128}{35}$

Step 2.2.1.3.3

Move the negative in front of the fraction.

$z = - \frac{128}{35}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{128}{35}$

Decimal Form:

$z = - 3.65714285 \dots$

Mixed Number Form:

$z = - 3 \frac{23}{35}$