Basic Math Examples

$18 - \frac{1}{28} \cdot (2 z) = 9 - \frac{1}{28}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Move the leading negative in $- \frac{1}{28}$ into the numerator.

$18 + \frac{- 1}{28} \cdot (2 z) = 9 - \frac{1}{28}$

Step 1.1.2

Factor $2$ out of $28$ .

$18 + \frac{- 1}{2 (14)} \cdot (2 z) = 9 - \frac{1}{28}$

Step 1.1.3

Factor $2$ out of $2 z$ .

$18 + \frac{- 1}{2 (14)} \cdot (2 (z)) = 9 - \frac{1}{28}$

Step 1.1.4

Cancel the common factor.

$18 + \frac{- 1}{2 \cdot 14} \cdot (2 z) = 9 - \frac{1}{28}$

Step 1.1.5

Rewrite the expression.

$18 + \frac{- 1}{14} \cdot z = 9 - \frac{1}{28}$

Step 1.2

Combine $\frac{- 1}{14}$ and $z$ .

$18 + \frac{- z}{14} = 9 - \frac{1}{28}$

Step 1.3

Move the negative in front of the fraction.

$18 - \frac{z}{14} = 9 - \frac{1}{28}$

Step 2

Simplify $9 - \frac{1}{28}$ .

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Step 2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{28}{28}$ .

$18 - \frac{z}{14} = 9 \cdot \frac{28}{28} - \frac{1}{28}$

Step 2.2

Combine $9$ and $\frac{28}{28}$ .

$18 - \frac{z}{14} = \frac{9 \cdot 28}{28} - \frac{1}{28}$

Step 2.3

Combine the numerators over the common denominator.

$18 - \frac{z}{14} = \frac{9 \cdot 28 - 1}{28}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $9$ by $28$ .

$18 - \frac{z}{14} = \frac{252 - 1}{28}$

Step 2.4.2

Subtract $1$ from $252$ .

$18 - \frac{z}{14} = \frac{251}{28}$

Step 3

Move all terms not containing $z$ to the right side of the equation.

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Step 3.1

Subtract $18$ from both sides of the equation.

$- \frac{z}{14} = \frac{251}{28} - 18$

Step 3.2

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{28}{28}$ .

$- \frac{z}{14} = \frac{251}{28} - 18 \cdot \frac{28}{28}$

Step 3.3

Combine $- 18$ and $\frac{28}{28}$ .

$- \frac{z}{14} = \frac{251}{28} + \frac{- 18 \cdot 28}{28}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{z}{14} = \frac{251 - 18 \cdot 28}{28}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 18$ by $28$ .

$- \frac{z}{14} = \frac{251 - 504}{28}$

Step 3.5.2

Subtract $504$ from $251$ .

$- \frac{z}{14} = \frac{- 253}{28}$

Step 3.6

Move the negative in front of the fraction.

$- \frac{z}{14} = - \frac{253}{28}$

Step 4

Multiply both sides of the equation by $- 14$ .

$- 14 (- \frac{z}{14}) = - 14 (- \frac{253}{28})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- 14 (- \frac{z}{14})$ .

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Step 5.1.1.1

Cancel the common factor of $14$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{z}{14}$ into the numerator.

$- 14 \frac{- z}{14} = - 14 (- \frac{253}{28})$

Step 5.1.1.1.2

Factor $14$ out of $- 14$ .

$14 (- 1) \frac{- z}{14} = - 14 (- \frac{253}{28})$

Step 5.1.1.1.3

Cancel the common factor.

$14 \cdot - 1 \frac{- z}{14} = - 14 (- \frac{253}{28})$

Step 5.1.1.1.4

Rewrite the expression.

$- - z = - 14 (- \frac{253}{28})$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 z = - 14 (- \frac{253}{28})$

Step 5.1.1.2.2

Multiply $z$ by $1$ .

$z = - 14 (- \frac{253}{28})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 14 (- \frac{253}{28})$ .

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Step 5.2.1.1

Cancel the common factor of $14$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{253}{28}$ into the numerator.

$z = - 14 (\frac{- 253}{28})$

Step 5.2.1.1.2

Factor $14$ out of $- 14$ .

$z = 14 (- 1) \frac{- 253}{28}$

Step 5.2.1.1.3

Factor $14$ out of $28$ .

$z = 14 \cdot - 1 \frac{- 253}{14 \cdot 2}$

Step 5.2.1.1.4

Cancel the common factor.

$z = 14 \cdot - 1 \frac{- 253}{14 \cdot 2}$

Step 5.2.1.1.5

Rewrite the expression.

$z = - \frac{- 253}{2}$

Step 5.2.1.2

Move the negative in front of the fraction.

$z = - - \frac{253}{2}$

Step 5.2.1.3

Multiply $- - \frac{253}{2}$ .

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Step 5.2.1.3.1

Multiply $- 1$ by $- 1$ .

$z = 1 (\frac{253}{2})$

Step 5.2.1.3.2

Multiply $\frac{253}{2}$ by $1$ .

$z = \frac{253}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$z = \frac{253}{2}$

Decimal Form:

$z = 126.5$

Mixed Number Form:

$z = 126 \frac{1}{2}$