Finite Math Examples

$- 15 \frac{1}{8} \cdot z = 2 \frac{8}{9}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $- 15 \frac{1}{8} \cdot z$ .

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Step 1.1.1

Convert $15 \frac{1}{8}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$- (15 + \frac{1}{8}) \cdot z = 2 \frac{8}{9}$

Step 1.1.1.2

Add $15$ and $\frac{1}{8}$ .

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Step 1.1.1.2.1

To write $15$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- (15 \cdot \frac{8}{8} + \frac{1}{8}) \cdot z = 2 \frac{8}{9}$

Step 1.1.1.2.2

Combine $15$ and $\frac{8}{8}$ .

$- (\frac{15 \cdot 8}{8} + \frac{1}{8}) \cdot z = 2 \frac{8}{9}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$- \frac{15 \cdot 8 + 1}{8} \cdot z = 2 \frac{8}{9}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $15$ by $8$ .

$- \frac{120 + 1}{8} \cdot z = 2 \frac{8}{9}$

Step 1.1.1.2.4.2

Add $120$ and $1$ .

$- \frac{121}{8} \cdot z = 2 \frac{8}{9}$

Step 1.1.2

Combine $z$ and $\frac{121}{8}$ .

$- \frac{z \cdot 121}{8} = 2 \frac{8}{9}$

Step 1.1.3

Move $121$ to the left of $z$ .

$- \frac{121 z}{8} = 2 \frac{8}{9}$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{8}{9}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{121 z}{8} = 2 + \frac{8}{9}$

Step 2.1.2

Add $2$ and $\frac{8}{9}$ .

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Step 2.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{121 z}{8} = 2 \cdot \frac{9}{9} + \frac{8}{9}$

Step 2.1.2.2

Combine $2$ and $\frac{9}{9}$ .

$- \frac{121 z}{8} = \frac{2 \cdot 9}{9} + \frac{8}{9}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$- \frac{121 z}{8} = \frac{2 \cdot 9 + 8}{9}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $9$ .

$- \frac{121 z}{8} = \frac{18 + 8}{9}$

Step 2.1.2.4.2

Add $18$ and $8$ .

$- \frac{121 z}{8} = \frac{26}{9}$

Step 3

Multiply both sides of the equation by $- \frac{8}{121}$ .

$- \frac{8}{121} (- \frac{121 z}{8}) = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{8}{121} (- \frac{121 z}{8})$ .

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Step 4.1.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{8}{121}$ into the numerator.

$\frac{- 8}{121} (- \frac{121 z}{8}) = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.1.2

Move the leading negative in $- \frac{121 z}{8}$ into the numerator.

$\frac{- 8}{121} \cdot \frac{- 121 z}{8} = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.1.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{121} \cdot \frac{- 121 z}{8} = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{8 \cdot - 1}{121} \cdot \frac{- 121 z}{8} = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{121} (- 121 z) = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.2

Cancel the common factor of $121$ .

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Step 4.1.1.2.1

Factor $121$ out of $- 121 z$ .

$\frac{- 1}{121} (121 (- z)) = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{121} (121 (- z)) = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.2.3

Rewrite the expression.

$- - z = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.1.1.3.2

Multiply $z$ by $1$ .

$z = - \frac{8}{121} \cdot \frac{26}{9}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{8}{121} \cdot \frac{26}{9}$ .

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Step 4.2.1.1

Multiply $\frac{26}{9}$ by $\frac{8}{121}$ .

$z = - \frac{26 \cdot 8}{9 \cdot 121}$

Step 4.2.1.2

Multiply $26$ by $8$ .

$z = - \frac{208}{9 \cdot 121}$

Step 4.2.1.3

Multiply $9$ by $121$ .

$z = - \frac{208}{1089}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{208}{1089}$

Decimal Form:

$z = - 0.19100091 \dots$