Basic Math Examples

$y = (\frac{9}{5} \cdot (d z)) + 32$

Step 1

Rewrite the equation as $\frac{9}{5} \cdot (d z) + 32 = y$ .

$\frac{9}{5} \cdot (d z) + 32 = y$

Step 2

Simplify each term.

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Step 2.1

Multiply $\frac{9}{5} (d z)$ .

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Step 2.1.1

Combine $d$ and $\frac{9}{5}$ .

$\frac{d \cdot 9}{5} z + 32 = y$

Step 2.1.2

Combine $\frac{d \cdot 9}{5}$ and $z$ .

$\frac{d \cdot 9 z}{5} + 32 = y$

Step 2.2

Move $9$ to the left of $d$ .

$\frac{9 d z}{5} + 32 = y$

Step 3

Subtract $32$ from both sides of the equation.

$\frac{9 d z}{5} = y - 32$

Step 4

Multiply both sides of the equation by $\frac{5}{9}$ .

$\frac{5}{9} \cdot \frac{9 d z}{5} = \frac{5}{9} (y - 32)$

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 $\frac{5}{9} \cdot \frac{9 d z}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{9} \cdot \frac{9 d z}{5} = \frac{5}{9} (y - 32)$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 d z) = \frac{5}{9} (y - 32)$

Step 5.1.1.2

Cancel the common factor of $9$ .

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Step 5.1.1.2.1

Factor $9$ out of $9 d z$ .

$\frac{1}{9} (9 (d z)) = \frac{5}{9} (y - 32)$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 (d z)) = \frac{5}{9} (y - 32)$

Step 5.1.1.2.3

Rewrite the expression.

$d z = \frac{5}{9} (y - 32)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{5}{9} (y - 32)$ .

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Step 5.2.1.1

Apply the distributive property.

$d z = \frac{5}{9} y + \frac{5}{9} \cdot - 32$

Step 5.2.1.2

Combine $\frac{5}{9}$ and $y$ .

$d z = \frac{5 y}{9} + \frac{5}{9} \cdot - 32$

Step 5.2.1.3

Multiply $\frac{5}{9} \cdot - 32$ .

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Step 5.2.1.3.1

Combine $\frac{5}{9}$ and $- 32$ .

$d z = \frac{5 y}{9} + \frac{5 \cdot - 32}{9}$

Step 5.2.1.3.2

Multiply $5$ by $- 32$ .

$d z = \frac{5 y}{9} + \frac{- 160}{9}$

Step 5.2.1.4

Move the negative in front of the fraction.

$d z = \frac{5 y}{9} - \frac{160}{9}$

Step 6

Divide each term in $d z = \frac{5 y}{9} - \frac{160}{9}$ by $d$ and simplify.

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Step 6.1

Divide each term in $d z = \frac{5 y}{9} - \frac{160}{9}$ by $d$ .

$\frac{d z}{d} = \frac{\frac{5 y}{9}}{d} + \frac{- \frac{160}{9}}{d}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $d$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{d z}{d} = \frac{\frac{5 y}{9}}{d} + \frac{- \frac{160}{9}}{d}$

Step 6.2.1.2

Divide $z$ by $1$ .

$z = \frac{\frac{5 y}{9}}{d} + \frac{- \frac{160}{9}}{d}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Simplify each term.

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Step 6.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$z = \frac{5 y}{9} \cdot \frac{1}{d} + \frac{- \frac{160}{9}}{d}$

Step 6.3.1.2

Multiply $\frac{5 y}{9}$ by $\frac{1}{d}$ .

$z = \frac{5 y}{9 d} + \frac{- \frac{160}{9}}{d}$

Step 6.3.1.3

Multiply the numerator by the reciprocal of the denominator.

$z = \frac{5 y}{9 d} - \frac{160}{9} \cdot \frac{1}{d}$

Step 6.3.1.4

Multiply $\frac{1}{d}$ by $\frac{160}{9}$ .

$z = \frac{5 y}{9 d} - \frac{160}{d \cdot 9}$

Step 6.3.1.5

Move $9$ to the left of $d$ .

$z = \frac{5 y}{9 d} - \frac{160}{9 d}$